Arf,
The only time I would budget more than $8 or $9 mil is if I need a Fielding Instructor and there are only a few available. Otherwise, anything over that is a waste of budgeted dollars. You should never have to pay the asking price for any of the ML coaches (except for when they are asking for the minimum). I always offer less than half the asking price and always get a PC, HC and BC cheaply. There are enough available that you don't need to overpay for those coaches. And as tec pointed out, you can always promote a minor league coach, or offer a minor league coach a big league offer.