Thanks for the suggestion. icynene looks cool.
But it's not really a DIY solution, and I've got zero budget for trades, for now.
So I think I'm going to use the "Great Stuff" foam on any small gaps, paint (spray) a sealing latex primer over everything, put up something like tyvek, and then staple batts of insulation. From what I'm reading here and elsewhere, this is probably the best DIY solution available to me.
Then I'll built the second wall, run power etc through it, and drywall.