It depends on how much you want to do yourself / how much stress you want.
I would look at going with either medium sized contractor who offers Design and Build or employing a project manager / surveyor. You will need Building Regs at least maybe planning depending on size / works , local planning restrictions etc.You will also need a structural engineer.
If you have an architect / surveyor helping you with plans etc ask them if they could recommend any contractors.
If your going down the subby route get used to rearranging everybody all the time and make sure every knows what they are doing and in what order.
Good builders should be busy, wait for a good one.
Regarding quotes make sure you have the information for the builders to quote on, and make sure you at least let them think its worth there while. Non of this I will buy the materials cheap etc . Why should they work on your job for a pittance if they can be down the road making some money!