I would say that you should shoot for 10 (+/- 2), depending on how competitive you are as an applicant. Now, I did not say that depends upon how high your numbers are! Esp when applying to residencies, it is no longer simply a game of numbers...but we can discourse on that in another thread. In all, for most folks, around 10 is reasonable, assuming you applied to a set of programs for which you are competitive, and that will be about as much as most folks can afford to travel to anyhow. It gets damned expensive &, as I understand it, programs are not paying for nearly as much stuff (hotel & airfare) as they did when I applied 2 years ago.
Prelim years - again, predicated on applying to programs that you are competitive for - I would say 3 to 5 would be more than sufficient. To save on $$, I only agreed to interview for prelim years at places I had already secured anesth interviews. With a family, I was not willing to move somewhere for 1 year only to pick up & move again.