I know the Bullet Hole rents handguns (as well as eye/ear protection) for use on their range. It's been a few years, but I used to go there fairly regularly. It's a great way to try out different weapons to find one that suits you best. I think they're around $8-$10 for a session.

All you have to supply is targets and ammunition - which, of course, they will be happy to sell you, but I think their prices were reasonable.