Univega Gran Turismo, Cannondale Synapse, Bianchi Aquiletta Folder
If it's one of the twenties with 406 size wheels, then pretty much any old-school BMX rims would work. I rebuilt my wheels with Alex DM24's for three reasons (also Sun CR-18's would work).
1) They are cheap.
2) They have eyelets.
3) They are double-walled for strength.
This is a good opportunity to learn wheelbuilding; you want to reuse your hubs. I doubt anybody has pre-built wheels for an R20- I certainly couldn't find any. Modern BMX wheels have axles that are too thick, and finding a 3-speed hub version would be needle-in-haystack.
A quick answer is not easy. It depends of ridingstyle and also how you want the bike to look. There has been a l o t of threads on this bike, so If you search the forums you can find out what others is using.
I`we got two similar bikes (different brand) and since I want them to be beater/utility bikes I use BMX front wheel and BMX rear rims and Nexus7 hubs.
You can also find that some peopel build them up as road bikes with much narrower rims and high psi tyres.
Some of us is lucky to have plenty dumpster bikes available. If you need to buy it is more important to get the rght thing first.
As said already there is two wheelsizes both called 20".
I suggest you post some pictures if you can. We like pictures . Best way to get attention and plenty feedback.
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...