Jess, don't get mad. The title of your post is "home addition," not "minor repair." You mentioned that you weren't going to have it permitted, so that is the reason that the people responded to that item. If you had not mentioned that part, no one would have brought it up. You did not specify the cost, so there's no way to comment on that. Besides, costs vary widely for different parts of the country, so asking it would not be useful.

For recommendations, you can ask people in your neighborhood who have recently had work done. You can ask real estate agents for recommendations. You can look on bulletin boards or websites (my area has a neighborhood blog and people frequently post "know any good contractors"-type questions). The main thing is to get references, check them out, interview the potential contractors, make sure they are bonded, etc.

Personally, I would want to make sure that the electrical work is done by a licensed electrician; same for plumbing. Washers and dryers require beefed-up electrical systems and specialized plumbing. If your dryer is gas, then it's even more important to make sure it's done correctly. No cost savings in a job that needs to be re-done or turns out to be dangerous. It sounds like a bigger job than a simple shed that would require a guy with a nail gun.

Best wishes for a successful repair or whatever it turns out to be.