Hi Rema,
Get their License and Insurance as a must, and then actually check them. Most states have a license search page you can check.
Small Contractors: Online Reviews, Photos of Work. If your work requires they provide materials, ask them to provide product data sheets, install instructions, and if applicable Operations and Maintenance paperwork. Most of these are readily available even on home depots website, but if they can't/won't provide them to you or provide them in a sloppy fashion you can expect similar from their communication on a project. It's a way to test for professionalism, doesn't necessarily mean they aren't good at the actual work, but worth asking for. Referrals work but only if you trust who you are talking too. Best thing you can do is plan on their work being 10-20% more expensive then advertised, if they stink you have it covered and try the next guy. Honestly, it is some trial and error at this level, and even if you get a great experience once, doesn't mean you will have a great one next time.
Assuming you have the volume of work to be talking to Larger Contractors: Ask for a COI naming you/your business as additionally insured (would recommend with all contractors, but most handyman won't know what you are asking about). Do not sign their quote ever. Create your own contract or PO order form, send to contractor to sign. The language describing the work should reflect your understanding of the work, or reflecting plan documents/spec. Union/Non-Union is a big deal at this level. Sometimes you can get the same crappy workers under different companies if they keep pulling them from the hall when its a large job, so you want to ask them how they are staffing the job, with current employees or pulling new ones from the union, partnering with another shop. Often they won't have the staff and will subcontract with another shop for additional labor. Meet the foreman/project manager as part of any final budget conversation. Its always wonderful when a project starts and the estimator does a Cheshire Cat impression and the PM is stuck with a lousy budget and tries to milk for change orders to fill up the budgets gaps. If the PM was part of the budget/quote discussion(s) (or at least the last meeting before contracting) then they don't have as many "reasons" for change orders. Plus it just helps get you all on the same team. Flat out to their face ask your contractor what's wrong with the plans the Architect/Engineer designed. They WILL tell you and you can save yourself some cost in change orders later on by addressing some of the issues now, if they clam up, be very afraid. They want to write change orders to you for all the plan gaps they know exist. Contractors love complaining about crappy design work on plans and will basically give away the farm on where the change orders that aren't earned (earned = you making a changes to the plans after contracting) will come from. Also ask them what they see as the biggest risk on the project for their scope of work. Ask them in person if this is a go to work number, and that they won't have 20 RFI's pending change orders for you five minutes after you hand them a contract. Ask them if there are any lien's on projects they contracted on, investigate if so. Being able to talk to the ultimate decision maker is really important at this level. If you the owner, can't talk to their president/owner directly to resolve any nasty disputes, then lawyers get involved and it gets ugly. I would advise against working with board run Contractors (or where the controlling power is distributed) because nobody wants to take risk in those situations and everybody becomes a lawyer real fast. Generally you want to have someone on their end who is empowered to speak for the company so you can resolve any sticky items quickly and with one decision maker.
I really like @Patrick Page multiple quotes comment. Get three, ask questions each, it will help shake things out. A good tip for the small stuff is to ask, who helped you the most while quoting? Asked the good questions? Was on time? Easy to reach? Might be they are the best option even if their quote is 1-5% more. On the big stuff, if someone gives you deal, you vet the crap out of it, and unless you have a very good reason for saying no you take it. You burn bridges with large contractors otherwise, and they might not bid your next job as estimating is a cost they can't recover if they don't get the work.
Estimating/Quoting - from my own experience as someone who solicits quotes, and provides them. I receive quotes form subcontractors, but build quotes for clients as a General Contractor. At some point all contractors will stop, or get real lazy about updating quotes/estimates if the job isn't locked in. They don't get payed to quote, just do the work. So every time they spend 30 minutes pricing something different they have to make money up on the actual work. Their margins get smaller the longer they price, so if you are asking for small time work, say $2,000 or less, don't expect somebody to spend 5 hours of their week repricing the same work to you with 20 different options. Eventually you become not worth the time/effort to serve. Also, give a good impression as somebody a contractor wants to work for. If you are a jerk, stupid, critical, or a lawyer, expect the cost to go up 10-15% just for the hassle of dealing with you. If I know that when I quote, it is absolutely built into the price, don't make the assumption that everybody is absolutely dying to work for you. When I do a site visit for a quote, it's an interview of the work and client for me, almost as much as it is for you. A good contractor will have a decent amount of work, and will have some walk away power. Bad clients usually equal bad jobs so keep that in mind when dealing with your contractor too.
