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?
As for time-tested and trusted brands in the hosting industry can recommend these hosts:
Crookservers.com, Mddhosting.com and Hostforweb.com
There are literally thousands of hosting services to choose from and you may be tempted to simply go with the least expensive option.