Just lost my first [long] reply to this. Agh!
Ok - short version.
Alloy rims are easy to find for n-american twentys as they're the same diameter as bmx and most small kids mtb bikes. You can get 'name' brands in this size as it's also a popular size for folders and recumbents - Alex rims, Velocity and Sun being good brands. You can get them online from specialist shops like Gaerlan http://www.gaerlan.com/bikeparts/par.../wheelbmx.html
but a normal local bike shop should be able to help too. Or you could look out for a cheap whole bike on ebay or craigslist and cannibalise it for the parts you need.
Be sure you get rims with the same amount of spoke holes. I think the standard on a twenty is 28 but I may be incorrect - check first!
If you're building into the standard hubs they are usually pretty low-mileage and likely only need a clean and regrease.
Since you're going to upgrade to alloy rims, you should probably get some new brake pads as the standard rubber ones are terrible in the wet - most people on here would probably recommend Koolstop Salmon pads for a small wheeled bike. Probably a good idea to fit new cabling too.
Tyres are a matter of taste and function, but there's a whole heap of tyres for that size that will fit from fast road slicks, puncture-protected commuting / touring models to knobbly off-road and dirt. The widest of the wide may give clearance issues, but the frame is pretty adaptable (euro ones use the taller 451 size) so you shouldn't within reason run into any trouble. Search this folding forum for many empassioned threads on tyre [tire] choices....
If you want more speed you could upgrade to the bigger 451 size - rims and tyres are harder to find, but the tyres you can get are high pressure and fast, and the rims usually narrower. One upside to doing this is you can fit shorter-reach, more efficient 'stoppier' brake calipers that improve safety with their better stopping power (shorter brake arms = more stopping power for the same amount of effort on the brake lever).
I think that's it for now - enjoy your bike - and if you have the time and inclination I do advise you have a go at building the new wheels yourself - it's really good fun and you can feel really proud when you're riding them...
[see my twenty linked in my sig]