This is a complicated topic and is bound to change over the years. GSResident has catalogued his experience at opening a Plastic Surgery practice and I find that a lot of the information is relevant to any private practice:
http://forums.studentdoctor.net/threads/first-2-weeks-in-practice.542695/
What my partner did was to develop a marketing plan which showed the lack of coverage in our specialty in town, the training that she had that no one else in town at that time had, and she shopped it to local hospitals for assistance. She did not have a rich uncle or anyone to help her with start-up costs; one of the local hospitals provided it to her, much as you would a salary guarantee. However, by way of full disclosure, she did have a husband who had a good salary working for Intel to help her through those first few lean months.
Surgical practices tend not to have a lot of overhead; most of it will be spent on employees or any capital expenses (if you have equipment like an ultrasound in your office) and your EMR. You aren't going to be stocking medication, vaccines, EKG machines, etc. that an FP would.
In terms of "splitting call" and number of physicians, that is up to you. The more physicians there are in the practice, the less call you will have, but the more patients calling during each call day/night. We started with just us two and although a breast onc practice does not have a lot of "have to go to the hospital" type of call, the patients are needy so there can be a lot of calls. Now we have 6 partners and we split the call on weekends and holidays, with each individual surgeon covering their own office during the week. It works well for us but the weekends on call are certainly busier than it used to be with just the 2.
The true solo practice is difficult. My best friend is in a solo Plastics PP and she never has any time off, refuses to ask anyone to cover for her except when she goes to conferences (and then she still takes the calls) and is constantly busy.