How long has the host been around, it’s beneficial if they have been established for some time, but this doesn’t mean rule out the really new ones but if you are going to choose a newish hoster, ask your self how are you going to feel if your site just disappears and you have no chance of getting it back?
Many of the hosts promise huge space and bandwidth because they know most customers don't use as nearly as they signed up with their hosting account. But if you really need an amount of space or bandwidth you thought you were entitled to, there might be a problem.
I'd probably also look for a company which has been around for a while with good support. Probably using CloudLinux and not unlimited everything, so that every individual reseller can't overload the servers with hundreds of badly managed accounts. That being said the response time to that kind of issues determines a lot too of course.