There is no consistency - much depends on the backlog at the FRS as well as other slots available. As a former Marine Student Control Officer, I used to get my billets from the company grade helicopter monitor at HQMC and then, in consultation with the other HT Marine Student Control Officer, we would assign these on the spot. Generally, it went according to what was available, your grades, and your preference. Occasionally, we would slide some stuff - not so much a "quality spread" like at TBS but to prevent SNA's from being shafted with something they really did not want.
SNA's selections tend to boil down to two things: location or platform. If we can get you both that's great, however we do work hard to make sure you get at least one and therefore are not miserable. Most Marine students tend to want Cobras when they show up at the HT's but by the end of HT training that percentage has slid after the SNA's talk to the IP's. I would generally say that it is neck and neck between Cobras and 53's for the most popular - PhrogDriver might have some more up to date info.
As for the total number of slots: there are 14 CH-46E squadrons of 12 aircraft each, 6 squadrons of CH-53E's at 18 aircraft each, 3 (or 4?) squadrons of CH-53D's with about 12 aircraft, 6 squadrons of skids with about 18 Cobras and 9 Huey's each - the squadrons aircraft numbers are only an approximation. You can do the math.