Completely agree with DavidH - avoid free. You always get what you pay for. Hosting is very expensive for a company when done properly, so if they're not charging you then they're cutting back massively somewhere. Places like GoDaddy make up for it in bulk and they typically run a lot of virtual servers for the individuals who pay for a "unique server". That reduces their costs while not skimping on quality.
Things to look for:
Uptime: if it isn't what we call "dot four" or 99.9999% uptime then they're skimping somewhere and/or have some serious problems.
Bandwidth: many places are now offering "unlimited" bandwidth but if you're expecting a lot of traffic, you'll want to look for hidden fees associated with massive bandwidth. There are different names for them like 'excessive upload' fees. Basically a place that has such fees has shoddy business practices.
DB support: do they use SQL or Oracle? Do they support DB problems? If they support other DBs like MySql or DB2, that's not a bad thing but it depends on how DB intensive the site will be. If you're not sure, you can PM me (or call since you have my number) but generally speaking most sites are not DB intensive.
Tech support: can you call them at 3am and get a live person that isn't being woken up? Like David said, typically you won't have to but its a good question to ask because you just never know.
Odds and ends: I prefer a place where I can build the site on my own without having to use some trumped up application they bought or set up to create a website. That makes the tech support less relevant (I wouldn't want to support some idiot's idea of a self-made website) but I know how to code and I'm fussy when it comes to that sort of thing. That doesn't mean those applications don't work or have value, but how willing are they to work with you for something non-standard will tell you a lot about the company. I recommend talking to someone. If you get a good feeling and all the other things check out, then go for it.
I like BlueHost too and let's face it, GoDaddy isn't the biggest name in the business just because of their "wardrobe malfunction" commercial.
"When the mob and the press and the whole WORLD tell you to move, your job is to plant yourself like a tree beside the River of Truth and tell the whole WORLD:
'No, YOU move.'" - Captain America
It's still the same old story
A fight for love and glory
A case of do or die.
The world will always welcome lovers
As time goes by.
- Herman Hupfeld
Veritas et Lux et Vitae