Agreed, yet going with a big time host is usually good, there are people out there that meet all these requirements are are not as big as say hostgator, bluehost, and the likes. So don't let size be the major deciding factor, if you see a host you like, ask questions. You'll be able to figure out which ones are good or not.
Respond time of support ticket, as short as possible. Server Uptime, as high as possible. Server speed, as fast as possible.