Well you should first know how large of the addition and also, what your heat pump can handle first. Because, that can be the downfall right there. Also, MAKE SURE TO GET THE PERMITS YOURSELF from the county. Most contractors (not us) but most will charge for a "runner". So get your ducks in a row first and then proceed.
1) What is your budget? You should always base it around that.
2) Ask how long they have been in business. Once they tell you, ask them, their basic price on say a 24x24 edition or whatever.
3)Time Frame. Make sure to ask the time frame. Because some builders that I know will take forever and a day because they think they can charge you overtime. Dont let this happen
4) Ask them for references of customers. Ask them to give you 5 on the spot. Once that is given to you, then you pick and choose which ones you want, which in turn gives you the higher up, because they will not be able to call all the customers fast enough.
5) Ask them the material size..such as will it be 2x6's instead of 2x4's. and so on.
I can give you so much more. But also, check out prices at Lowes, or Home Depot also. A good contractor will welcome the idea that you have done your homework and some leg work.