We recently completed a project on a very old house. We did it for time and materials, which is unusual for us. I was very glad we did it that way. If I had been pressed to bid a firm price, I would've bid around $15,000. However, after all was completed and changes made we charged $42,000 using T&M. I'm telling you this not to scare you, but to show how different things can be from the plans to actuallity in an old house. Also, the owner of the house we did constantly changed things and the original plans looked nothing like the final project.
If I were the owner(you), I would want a fixed price. Just make sure everyone is clear exactly what is expected and what happens if a change comes up or if something unexpected is found in the walls. Check the company out completely. If they seem too cheap, they probably are and will come back for more money.
