Make sure they are licensed (State DPOR [Dept. of Professional Occupation and Regulation]) and insured (business liability w/ a min. of million dollar coverage).
For references, ask for the LAST three jobs they did. It's easy to find 3 people satisified with just about anyone. But, the last 3 jobs should give you a more balanced representation.
You are going to be hard pressed to find a contractor who can guarantee a time-line or will sign on to be financially responsible for things being back-ordered or lots of work changes. That's not really done.
EXPECT it to take longer and more money--especially w/ an addition. The contractor has no idea what he's going to find when he takes your walls/roof down--if the wiring has not been up to code, that's a whole 'nother can of worms not priced in or built in time-wise. And you can about gaurantee there will be some issue like that. So, leave extra money and time in your budget and plans.
You can call supply houses in your area and ask if the contractor is up to date on his accounts. If he's delinquent and in financial trouble, you could get really screwed.
You can also ask the contractor how much work they sub out. If they do most of the work themselves, scheduling might be easier.
If they use subs, make sure it's in the contract that ALL subs carry liability and workman's comp OR are covered under the general contractor (not likely, at all)--because YOU can be liable for *their* injury or if an unlicensed sub burns your house to the ground you may be SOL.
And get at least several estimates and compare apples to apples--the bottom line price can be very deceiving--make sure that the contracts include the same things. Lots of contractors will come in cheap, but will intentionally leave things out so they can do a bunch of change orders in the end for lots more money--but they're things that need to be done regardless, and they know you're not going to go getting estimates for "a la carte" items once the job is underway. Like, contractors who contract for tiling "two shower walls" at x dollars. Well, yeah, but you pretty much need that 3rd wall tiled, too, you know?

So, his discounted price might not be much of a discount after he gouges you for that 3rd wall.
Good luck! Trust your gut, too! Most contractors are hard working honest folks looking to do good work. But, there are a handful of shady people out there. And for whatever reason, even the good ones seem to have issues about time frames and returning calls! It's just kind of the law of the land.