I bent a rim, what kind of new rim should I buy?
You say you want to replace the rim, but unless the hub is something special, or you're going to rebuild the wheel yourself, it's probably cheaper to replace the whole wheel. 

If you're replacing the rim, apart from approximately matching the rim width (see Sheldon Brown) you also need to match the number of spoke holes if you want to reuse your hub, and it's a good idea to replace the spokes that have been damaged. If you have rim brakes also need to make sure your new rim has a braking surface. 

If you're replacing the wheel, you need to match the hub type and size. The type could be quick release (QR), thru axle (of which there are a couple of sizes) or nutted with dropouts (again multiple sizes). The relevant size is the over locknut distance - the width of the hub. You also need to know whether your old wheel used disc or rim brakes, and if did, what type and rotor size.