If you are looking to stick with the tires you have, a set of standard 20x1.75 rims will probably be the most inexpensive and easiest to find.
If the rear freewheel/cassette looks super small (9T) then that's fairly modern (New School) and you will likely be able to find a parts bike on craigslist or something that will have what you are looking for. Otherwise, 16t freewheels were pretty standard in the old-mid school stuff. Often available used with minor servicing required. As others have said, look for aluminum hoops, and if possible, multi-wall for strength. Old single wall cheap steelies are often not even worth using unless its "period correct". You will likely have 36 spoke options or 48 spokes... 48s are typically for trick riding as they are a little stronger. 36s are race/standard equipment on a lot of stuff and likely more common to find used if that's your thing.
Out of curiosity, what kind of mags are on the thing? I love mags. I have Skyways, O.G.Ks, and Troxel Trakmasters on some of my bikes... I think i just like them because they require less maintenance haha.