Former enlisted here. (83-89)
I signed up as a Data Systems Technician, shortened to “DS” for conversational purposes. (This is called your “rating”, further defined by a number code called an “NEC”. The other services call it your MOS.) After I got out, this rating was merged into a couple others (like Electronics Technician, or “ET”).
I went to Boot camp, then Basic Electronics School in San Diego, and “A” school in Vallejo, California. I did not get to select any other base or duty for this period, because I had to go where the schools were.
Once I passed “A” school (and if I flunked those schools, I would have been shipped out to the fleet as a non-designated Seaman), I picked my next school (my class picked in order of grade point average: highest grade point average got first pick of the available schools, etc), which ended up being located on NAS Key West.
Once again, in grade point average order, the graduating class picked from the available ships/duty stations. I got a carrier based out of San Diego.
From this point forward, an enlisted’s rotation is determined by their NEC, their pay grade (rank), and what billets happen to be open for those. In my case (a third, then second class petty officer), I had to do 6 years at sea, 2 years ashore (I expected the shore duty was going to be as an instructor at one of the “A” or “C” schools).
There is a person called a “detailer” whose sole job it is, to try and match up people due to rotate with available billets for that NEC & pay grade. So I would have to get in touch with the detailer, and he or she would inform me of my choices. I would get to pick from those. There is probably a whole unwritten code in how to get on the good side of your detailer, but I got out of the Navy before I was due to rotate off my first sea command. 