You can list as many units are you want on your "dream sheet" 1/c year. I believe I listed between 17 and 21 units. In completing your wish list, you can give the assignment officers (officers at Coast Guard Personnel Support Command) a good indication of where you want to be....
I picked white hulled cutters on the east coast. I listed Gallatin and Dallas as my top two (both 378's). Dallas went from having 6 or so billets to 1. I got my third choice, a 210'. I was very happy with that selection.
From the Coast Guard Academy, you will generally have three choice areas.....
Sector, Cutter, or Aviation.
After that first tour (two or three years) your "shopping list" will reflect a greater range of choices, including grad school, various operational and staff billets etc. Your Officer Evaluation Reports (OERs) and command recommendations will provide the major support for your transfer season hopes. Needs of the service, the assignments of other officers and your overall job, as well as the work of the assignment officers or "detailers" will dictate where you go.
What's great is, the incumbant officers in the positions you are looking are are available, so you can call them and ask questions...get a good feel for where you may want to go. It's "trying" but it's interesting and a part of life there and in the fleet. It's also fun to see where you classmates are stationed and where they transfer to.