These could be among provisions included in any Scottish constitution if people voted to leave the UK.
That constitution could also bar the possession of weapons of mass destruction and set out what terms would have to be met to go to war, Alex Salmond suggested.
These are some of the guarantees Nationalists would want to see included, although the constitution would be drawn up in consultation with the other political parties and wider Scotland.
The UK is the only country in Europe without a written constitution "protecting its citizens", the First Minister said.
"Scotland, an independent Scotland, would be a modern democracy and a modern democracy should have a written constitution," he told BBC Radio Scotland.
"The sort of ideas the SNP would contribute to a process that will engage all of Scotland, as well as all of the Scottish political parties, are things like protection in terms of free education.
"Scotland pioneered free education hundreds of years ago. We have a policy and we have restored free education but there should be a constitutional protection."
The constitution should include the "right of every Scottish family to have a home".
He said: "Again we've got statute on that but shouldn't there be a constitutional protection?
"The right to free Scotland of nuclear weapons: shouldn't there be a constitutional provision banning the possession of weapons of mass destruction in an independent Scotland? That would be a good thing.
"Shouldn't there be a provision in the constitution which says these are the provisions which have to be met before Scottish forces are to be committed to an international conflict."
Issues such as these are "the sort of things which you can put in a modern constitution which engages the citizens and are the big issues of the day".