RH 7 would run perfectly fine. However I believe you're confusing RH with RHEL which is the flagship and current release from Red Hat Inc. (although it's not free anymore - you have to pay for support).

I'd suggest you install CentOS which is a distribution based on RHEL... CentOS even claims to be 100% binary compatible with RHEL.

Fedora is also RHEL-based but most of its bundled software is beta, experimental, RC, unstable, etc so there may be a few bugs here and there.