The problem is that I know all these wheels are not the same, but I don't know if the standards (or how many standards there might be) have names. I don't know what the standards are. I don't know if the cassettes are around a standard either. I don't want to buy a rim with the wrong parts for attaching the cassette that I have which fits on my existing rim. All of the freewheel and ratchet stuff is in the rim and it is keyed to accept a particular type of cassette, but I have no idea if those cassettes conform to a or multiple standards.

There is only bike shop near my house and I can't stand them. They are really rude. But I haven't found the right rim on Amazon, so I might have to bite the bullet.