Hey @Matthew Sutton
Having managed contracting firms before, the biggest piece of advice I can give you is: do your homework. What I mean is, know your state laws. For example: In California (where I used to work) a contractor can only ask for $1,000 or 10%, whichever is lower, as a deposit. So if any contractor is asking you for more than 10% to start the job, find out why. If he says it's for materials, offer to pay for the material directly. Even offer to meet him at the hardware store so he can pick out what he needs and you pay for it.
Make sure the contractor is licensed and bonded. Don't just take his word for it. Have him provide you with proof and then look up the license online and see if it's current and if there are any claims against him from either previous customer or subcontractors he didn't pay.
Ask for references and call them. Of course they're going to only give you the ones that are going to say nice things about them. But if he gives you two references and has been in business for 10 years, I would be uncomfortable with that ratio.
Finally, get a detailed proposal for the work he is bidding. If his bid says "Home remodel - $20,000". I'd trash it right away. A good contractor will itemize the entire job with prices for everything. You can then do some quick research online to see what the average cost for certain items is and if he's within range, then you can feel more comfortable in using him. You can even ask him to list out material and labor separately.
I tend to ramble so I hope some of this made sense and was helpful. If you have any other questions, feel free to ask and I'll be happy to help if I can.
Good luck!