I personally use Servage for now, until I can muster up the cash to get a real dedicated server. I've been happy with them. Plenty of space, and lots of bandwidth. RoundCube works perfectly fine with their setup; however, I don't think you can create email users via a web interface without using their system. But I'm okay with that.
HostGator seems to be a rather good company for some people. All depends on what you want. You can shop around for them. If you really want control, a VPS or dedicated is what you need.