I build for a living (industrial projects), so have a bit more experience than the average person, but will give you my two cents worth.
Starting your search looking for a "low cost" contractor is a big mistake.
What you want is an honest, reliable contractor. Forget the competitive bidding process, and just work with a good contractor to come up with plan to meet your needs and budget.
I most recently had a brand new vacation cottage constructed at a site 300 miles from home. This was a very pleasant building experience, it was completed very quickly, the workmanship is good, and there were no financial surprises or loose ends. Here is how I went about the process:
1. First created construction drawings and a very detailed written scope of work clearly explaining everything that I wanted. If you do not have these capabilities, hire a professional residential designer to help you out with this.
2. Every location generally has a large lumberyard where most of the residential builders acquire the majority of their supplies. Not Home Depot, Lowes or Menards, builders generally deal with the larger privately owned lumber yards because they have much better people on staff and are much more customer service oriented. Locate this place, then call and ask to talk to the manager of contractor sales.
3. When you locate this guy, share with him what you are wanting to build and ask him for a name or two of who he would suggest to do your project. Be clear with him that you want someone reliable, that pays their bills, and does what they promise to do. Likely he will give you a name or two with a strong recommendation.
4. Call the recommended contractor, tell him where you got his name, roughly what you are wanting to build and ask if this is something he might be interested in doing. If he's interested, set up a meeting.
5. When you meet, show him your plans, explain that your not interested in getting competitive bids, and that you simply want to partner up with somebody good that can get this project done quickly without a bunch of surprises or hassle. Explain that in the interest of not wanting to waist a bunch of his or his subcontractors time, please take a look at the plans and scope of work and put a quick ballpark budget number on it to see if it makes financial sense.
6. If the budget number sounds good, tell him so and ask him to firm up the pricing to an exact figure and put it all down in writing, including payment terms, who handles permitting, etc. If budget is more than you want to spend, share your budget number and ask if he has any ideas to get you your number? The point here is that you are trying to be respectful of his time, and trust and work with one guy, rather than competitively bid your way to a number.
7. When you get everything nailed down, don't be afraid to ask to see a couple finished projects or talk to a couple past clients prior to turning him loose. Any good builder will allow this. Also be sure to get copies of his insurance coverage prior to starting, and have you own insurance man take a look at it to assure you don't have any coverage gaps.
8. When the project gets underway, hold up your end of the deal to by making timely decisions, paying bills on time, etc. Scope of work changes once the project is underway will be costly for you, and a hassle for your builder, so get as much worked out in your original drawings and design as possible.
Building projects do not have to be a hassle. Select a good builder, trust his expertise and let him make some money. If you are not in the business, you have no business evaluating bids or proposals so forget the whole stupid competitive bidding scenario.
Good luck !