The CG is pretty much the only branch of the military in which you choose your own job, as long as you physically qualify and have the right ASVAB score. When at your first unit as a non-rate (either seaman or fireman) you have to wait approximately 4 months and then you can put your name on the school list for whatever Coast Guard rating you want. It doesn't matter if you're a seaman or fireman or have any skills pertaining to the rating. That's what the school is for. More frequently sought after jobs or those with less available overall billets (ME, Aviation, HS) have a longer waitlist naturally than something like BM or MK. You have to wait out whatever the wait is if you want to be that rate.

If you leave boot camp as an E-2 (the apprentice level) you will either be a seaman apprentice or fireman apprentice depending on what your unit needs. Sometimes if you really want to do one or the other your unit will even let your switch if there's a need. Once you promote to E-3, you become a seaman or firearm until you go to the A-School of your choice. That's all there is too it really.