General advice needed on new/reburbishing rims

I have a 1987 BMW 325i and the rims are pretty beat up. I think they're alumunium, aren't too shiny. I may only have the car another 5-10 years (though who knows, it runs great) - I see Rustoleumn paint as a possible do it yourself option that looks decent, but I do like a shiny look so maybe paint won't get that? Any thoughts on best ways to do it yourself, or best options for buying rims? (what are the general types of rims - do I need to find out what I have and specify aluminum or chrome or something else, so I get what I really want if I order online?).

Thanks.

If you want to go cheap, buy some cans of the high temp engine enamel paint in whatever finish you want, then lay down a tarp and spray an even coat of paint and wait 15min repeat with 2 more coats with 15min intervals and let them dry overnight. I did this on a z3 I had a long time ago and worked pretty good. Remember wheels must be clean. Hope that helps.