If you keep the original 125 (or 135) R12 tires, you'll be doing yourself a favor. Just about all the other tires are next to impossible to find.
There aren't many parts you can interchange on the Cooper/Austin minis, but
www.minimania.com has a good selection of rims/tires and common bits. Not too much though. Mr. Fiat is the only site I know of as well for stateside service/parts.