The woman soon to become the most powerful in Scotland opens the door of her Glasgow home with a wan smile.

It's a sunny November Saturday morning, the neighbours are out and about, and she's still on a high after receiving a standing ovation from 2000 supporters at last night's sell-out rally in Dundee. "Come in," she beams. "Peter's got the coffee on."

As Nicola Sturgeon pads in her stocking soles through to the lounge of the modern detached home she shares with Peter Murrell, her husband of four years and the SNP's chief executive, she looks remarkably relaxed and happy, though I detect a hint of fatigue beneath her flawless makeup.

After the gruelling independence referendum campaign, the very idea of embarking on a series of political rallies across the country would be enough to floor the strongest man. But not, apparently, the pint-sized Sturgeon. Elected unopposed yesterday as leader of her party at age 44, she is due to become the first female First Minister of Scotland on Wednesday following Alex Salmond's resignation on Tuesday. By the glint in her eye it's clear she's enjoying making political history: the scale of her sell-out tour is unprecedented in modern UK politics - 20,000 tickets were snapped up within hours of their launch - and it culminates with her appearance before an audience of 13,000 at the Hydro in Glasgow next weekend. Doesn't she find it exhausting? "This is the thing I most enjoy about my job, and when you love what you do adrenalin keeps you going," she says. "Standing in front of an audience, feeling the energy, is what it's all about. I could stay on stage and do that for hours." (It was a similar story at the Corn Exchange in Edinburgh the week before, and the Eden Court in Inverness a few days after our meeting; T-shirts bearing slogans such as Sturgeon: The Tour are selling out.)

Scotland's first rock-star politician - who, I am reliably informed, once favoured Doc Martens and the punk look in the mid-1980s - says it's not the adulation she thrives on, but the connection with the people. "Put aside that it's me doing it, the fact we got 2000 people talking politics on a Friday night in Dundee is incredible," she says. "Questions range from the NHS, jobs, fracking, what next after the referendum. For me, the vibrancy of a new democracy in Scotland is electric and it's carried by the momentum from the referendum. People who had never had any interest in politics before are really engaged."

The SNP has tripled its membership to more than 80,000 following the referendum, making it the third largest political party in the UK. Which means the baton she is about to receive from Salmond carries considerably more weight than might have been assumed after September 18's No vote.

"I feel a responsibility," she says. "We have got to harness and keep hold of that engagement, repay the trust that people are putting into the democratic process. You might say the increased membership will be difficult to manage, but I see a massive opportunity to change things, to close the gap between the people and the politicians. I hope it changes the way politics are done in this country. I want new members to encourage others in their community and workplace to join."

If that sounds like a new evangelism, she's unrepentant. "If your pal or neighbour is in the SNP you're more likely to listen to them than if you just turn on the telly and see me or Alex. The growth of membership is building a politically engaged community base that hasn't been there in my lifetime."

Sturgeon has pledged to be the most accessible First Minister since the Scottish Parliament was founded in 1999, and plans a monthly Facebook question and answer session with members of the public to bring them closer to the political process. That is also unprecedented, and marks another of the differences between Sturgeon and Salmond, her political partner of 10 years. "I'm a different personality from Alex, though I've made a conscious decision that I'm not going into the job thinking of what makes me different from him. Everybody knows my relationship with him is fantastic and I'd never criticise what he has done. I'm not going to rip all that up just to demonstrate that I'm not him. But the differences will become obvious."

Being an enthusiastic user of Facebook and Twitter is one of them. "Social media is natural to me, and it's a very immediate way of saying something. It's the way politics are done these days. In modern politics you can't ignore that even if you wanted to. I can't imagine doing politics without it." The only indication of this in her pristine home is the iPad which lies charging on a table. "Having said that, its immediacy is also one of its problems. You have got to be careful, because the temptation is to speak before you think. I've always applied the rule that you don't say anything on Twitter that you wouldn't say on television. And never, ever tweet after a glass of wine."

While she's been basking in the grassroots support of new and long-term party members, however, social media platforms have been crackling with menacing comments, some sounding very like death threats. Anti-SNP, anti-Salmond and now anti-Sturgeon sentiment is ongoing. How does she cope with it? "I've had particularly unpleasant stuff and it has been reported that I've had death threats. Twitter and Facebook give people who have always been out there a platform from which to hurl abuse, and all I can do is try to block it out and remind myself that tweets are transient and get lost in the ether after a few moments.

"I do mute people. It's a great facility because the person doesn't know you've done it, but many of my constituents use Twitter to ask questions so I try not to block people unless they're being racist, sexist or particularly rude. If it's just someone being strident and impolite, that's democracy. I wouldn't necessarily answer it, though."

Murrell has by now served us coffee and pastries, and is busy elsewhere in the house. When I interviewed the couple just weeks before their wedding in 2010, Sturgeon admitted she didn't cook and said her partner's steak and chips, spag bol and curry were the best. The names Rick Stein and Gordon Ramsay were among his chosen cookbooks. "It's my relaxation," he said then. I made myself unpopular by reporting that his fiancee couldn't distinguish between the basil and parsley plants growing on the kitchen windowsill. This time, I don't get near the kitchen. Has her culinary knowledge improved "I can make coffee," she insists with a giggle. "I'm not the greatest cook, but then I don't apply myself. Peter's steak and chips are the best, so I don't really have to. I'm not domestic but I do iron his shirts, that's my one domestic claim to fame and it makes up for all the things I don't do.

"Being a housewife is not important to me, but I'm never happier than when I come home and shut the door. I like being home. I'm not domestic in the sense of being good around the house like Peter. He also looks after the garden."

Born in 1970 and raised in the Ayrshire village of Dreghorn just outside Irvine, Sturgeon had an "ordinary" upbringing, attending Greenwood Academy in Irvine. It was at school at the age of 16 that she joined CND, then the SNP. She went on to study law at Glasgow University, graduating in 1992. She worked as a solicitor, latterly at Drumchapel Law Centre, before becoming an MSP in 1999. She now represents Glasgow Southside. Another difference between her and Salmond is that she has never sat at Westminster: she has been at the Scottish Parliament since its inception, and declares herself a "child of devolution".

She has said that Murrell, whom she has been with since 2003, is her "constant reminder that while the SNP is important to us both, other things in life matter as well". For his part, he has said that "loving Nicola gives me a feeling of completeness".

"He has his faults, though," she adds now with mock disapproval. "He's very untidy. When he cooks a meal it looks like a bomb has hit the kitchen and he leaves it like that. It tends to stay that way until he clears up."

Their conservatory dining room is crammed with photographs of Sturgeon's niece and nephew and Murrell's three nephews. The children often text their auntie "about everything and anything but certainly never about how I look on the telly or what I said". Spending time with their families is the most important aspect of the couple's lives outwith politics. They are party people, but not in the celebrity sense. They rarely go to the cinema, never go to the theatre and prefer to eat at home.

Will Sturgeon use the ministerial residence Bute House as much as Salmond did? "I will stay there while in Edinburgh, but I'm not going to be living there. I'll want to live in my own home. The advantage I have is that it's only 45 minutes away, unlike Alex whose home is in Aberdeenshire. Glasgow's my home, both personal and political. But when you're First Minister you're not only standing for one part of the country."

At this point I bring up the elephant in the room - the patter of tiny feet she reportedly mentioned in a newspaper interview about living in Bute House. "I said as a joke something like 'I'm sure the patter of tiny feet would brighten up Bute House.' It was lighthearted, " she says. "People ask me as if motherhood is something that at some stage you've made a decision about. It's not how these things happen." And we leave it at that.

When I first interviewed Nicola Sturgeon exactly 10 years ago this weekend, she was single and living in a flat in Glasgow city centre. She had just become deputy leader of the SNP and declared her intention of defeating the then First Minister Jack McConnell in the Scottish parliamentary elections in 2007 (her reputation as a nippy sweetie was sealed during her ding-dongs with McConnell at FMQs). Her other political rivals at the time were David McLetchie, Jim Wallace and Robin Harper - giants, at least physically, when compared with her 5ft 4in, size 8 frame (she'd just lost a stone following a diet). The high heels she adopted then - from Dune to Kurt Geiger - have remained a staple of her professional wardrobe. The killer patent scarlet six-inchers she wore at the rally in Dundee's Caird Hall are at the front door alongside a pair of slippers, reinforcing the impression that work and home are kept quite separate.

Today she's wearing her "at-home wardrobe": shirt, jeans and minimal jewellery, though her hair and makeup are perfect. She does her own styling, and her hair looks softer and more natural than it tends to on television or in print. Padding around her cosy home - all light carpets, pale walls, modern oak furniture - she's looking particularly slim. She's returned to a size 8-10 after losing "a fair bit of weight" during the referendum campaign, and hopes to keep it off. A cross-trainer upstairs isn't getting the attention it deserves, because of her irregular schedule; she acknowledges she can focus more easily on watching her diet than exercising.

"Seeing yourself all the time on TV or in newspapers is a good incentive to stay slim," she says. Every bad hair day, unfortunate facial expression and single ounce gain is commented upon, and social media only serves to encourage yet more comment; particularly so with women. One female online journalist recently said Sturgeon had once looked like "a dead ringer for Angela Merkel - all elephantine linen trouser suits, death row haircut and M&S shoes". Another described her haircut as a "Lego hairpiece", though more acceptable, perhaps, than the gelled spikes of her teenage years. In fact, she shops online at Hobbs and LK Bennett and will continue to do so. She will get no ministerial clothing allowance.

Declining the offer of a pastry, she sighs. "One of the most difficult things about being a woman politician is the derogatory comments about your appearance. I constantly read about the mess of my hair, my clothes or how I look. I have been reading it so long I'm inured to it, but I do get annoyed when I think about some young woman being put off a career in politics by it. That does make me angry: women should be positively encouraged. Having succeeded in having more women get to the top at the Scottish Parliament, you'd hope it would then be easier for the next generation of women to come through."

While Sturgeon enjoys the format of the public meeting, holding FMQs is a different matter altogether. "I'm not sure it's an experience you ever get to enjoy," she says flatly. "You never look forward to it. It's a stressful half-hour and very daunting. But it is the time your political opponents get to hold you to account. It shouldn't be a walk in the park, it should be tough. But I can't say I'm relishing that part of my job."

When she holds FMQs on Thursday for the first time in the top job, might we expect a brand-new look? She looks at me askance over her coffee cup. Er, that'll be a no, then.

"I have a high intensity period ahead of me over the next two to three weeks, when I'll get very busy," she says. "I'm really looking forward to it, but if I was a man I wouldn't have to worry about my wardrobe so much. Women have to plan ahead, think about what we're going to wear each day, assess if we need our hair done, angst over wearing the same thing two days in a row. Choosing what colour of tie to wear really isn't the same thing at all."

With that, the coffee cup is set down. She's off to hold a surgery in her local constituency, and it's clear she's back on full throttle.