Just for the sake of reason, here's why I choose the order I do:
Exposure protection:
Having a properly fitting and sufficiently insulation exposure suit keeps one warm and allows one to focus, more clearly, at the new tasks being learned. Secondly, the exposure suit has, by inherent design, more effect upon one's buoyancy. Becoming accustomed to the buoyancy characteristics of one's wet suit will help one "master", more quickly, control of buoyancy.
Renting different wet/dry suits can cause the diver to change, constantly, the amount of weight required to dive and can result in other areas of concern, such as trim.
B/C:
The b/c is an item that, while it has a more exaggerated effecty upon one's buoyancy when operated, has somewhat of a lesser effect while diving at depth. Purchasing the B/C early in the game allows the user to become intimately familiar, sooner, with all of the clamps, clasps, d-rings, pockets, etc., etc., etc. Familiarity with this piece of gear will allow the diver to complete simple tasks without effecting the buoyancy element of the diving equation.
Hereagain, renting a B/C will probably result in the diver using a different make/model of B/C in many cases and leading to confusion when trying to make adjustments.
Regs:
While many posters lambaste the quality of rental regs, they seem to be referring most frequently to those dive regs provided by operators in the warm, fuzzy areas of the world. For the most part, local dive shops do a pretty good job of maintaining rental regs. The LDS's fear of expensive litigation can be a good friend on the part of divers renting gear. The force required to get air from a reg is not a significant factor in buoyancy, and the new diver, without a great deal of experience in using differing regulators, will probably not notice the difference between one rental regulator and another.
the K