Dan,
I'm probably a bit out of date as I went through flight school 40 years ago, but assuming things haven't changed that much the system is not quite the way you think.
Everyone started off flying the same aircraft, in my case the T34. After that program and six weeks of strictly ground school, everyone made their selection on what they wanted to fly. Pretty much everyone chose jets over helicopters. Selection was made by grades and, above all, needs of the service at that moment. In my bunch a few went jets, but most of us ended up in the helicopter pipeline.
It wasn't 3 or 4 months later that everything changed and word came down that anyone who wanted jets could head to NAS Meridian. Surprisingly, only a couple took the offer, the rest of us had been around our second tour instuctor pilots to know that if you wanted to fly, helicopters was the way to go.
In jets you were lucky to get 20 hours a month, in helicopters 40 to 60 hours a month were pretty common. In fact, at one point those jet jocks who graduated flight school and reported to the RAG (replacement air group) at Cherry Point found themselves with a year wait as the training was horribly backlogged. Word went out once again that any jet jocks that wanted to start flying, there was a need at New River as a number of helicopter squadrons were short handed.
And, after your first tour, those pilots that were regulars or on unlimited active duty, had the opportunity to get transitioned from helicopters to jets and vice versa.
So, in short, who flew what, depended on where the seats were.