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Any FICO over 720, and you aren't going to find any better mortgage rate. CC debt is $0, only student loans and a car, so long as they are on time you're good to go.
A 30 day late from 2002 isn't going to hurt you. However, it is a good candidate for GW. Not many GW examples here, but there's a number of them over on creditinfocenter. Search there to get a feel. You can PM me if you like, and I can point you directly to several.
There are a couple of hard nosed lenders who probably wouldn't remove a late. But by and large an old late can be GWed away.