I coach throwing events in college and here's what my experience has taught me: Typically, rims are not sold separately of discs. If the rim of a discus is burred up and dented, it won't be competition legal at bigger meets like conference, regional or state/national championships. You'll have to check at weigh-in of every meet to be sure it's legal.
Somebody has already made the point that it's a VERY good idea to have practice discus and competition discus. I agree with this. We have 1-2 men's and women's discs that are used ONLY at meets. Everything else is for use at practice. If your expensive new discus is broken up too badly, it might be time to demote it to "practice discus" and buy a new meet discus to replace it.
Also, if your budget doesn't allow for too many "practice discus", there are a couple of other things you can do: Throw a larger orange cone. It's a very good substitute, if you can't get anything else.
As far as actual products I'd recommend, there are several pretty good discs that you won't break the bank on. They're all in the MF Athletics catalog.
First Place and Polanik both make pretty good low-end (pricewise) products: They're ABS Plastic sides with steel rims and they usually run about 35-70 dollars. Buying some rubber discus is another possibility. Those can usually be picked up for 20 dollars or less, a piece.
I hope this helps. Good luck with your season and your shopping!