You asked a lot of disparate questions. Each one deserves a separate answer. I'll try but you may do well to speak with a recruiter and visit a unit or two, of different types, near you.
First, if paying for college is your only motivation you may want to reconsider. Yes, the GI Bill is a great tool but keep reading the As to some of your other Qs to further answer this question indirectly.
Second, getting married is not a good idea just because "she wants to go with" you. In fact, it's a bad idea which can end in divorce and lost friendships. I don't know the personal situation between you and your girlfriend. Just keep in mind that "she wants to go with me" is not a good, solid foundation on which to build a marriage. I'm no Dr. Phil, personally can't stand the show, but I do think he woud agree with me on this point. You should both think this through very carefully.
Further, if you end up on a ship she'll be alone quite a bit of the time in a region of the US she may not necessarily acclimate to. This can swing either way, she may enjoy it. The comings and goings of a ship does strain many a relationship. Just something to keep in mind.
Third, "A" schools are designed to give you the basics for a specialty. There used to be avenues for on-the-job training (striking) to earn a specialty. I'm not sure if this still applies to many of the technical jobs available.
What year of college are you in? If you're close to your Associates it may enhance a resume for Office Candidate School (OCS) after just a short time of your enlistment. Definitely a good career avenue.
Don't take my above comments personal. I would give the same advice to anyone who mentioned possible marriage just to stay together. Your post makes it sound like a marriage of convenience - just not the best idea for either of you.
Don't limit your search to just the Coast Guard. There are five volunteer services which would probably love to have you. They all have plusses and minuses to serving.
Good luck in whatever you choose.