You will need a passport, even if you are just going to the Bahamas, Mexico or the Caribbean, etc. You can complete your entire passport application process at certain (not all)post office branches; the one in Summerfield on Hwy 301 (on the left; about 1 mile north of the Hwy 42 intersection) will do it all - including taking your photographs, in one visit, but you have to make an appointment; but less of a hassle in the long run; and once you have your passports, they are good for ten years before you have to renew them. You can get the P.O. phone # at
www.usps.com or or local phone book. There are probably other local P.O. branches that do this, but that is just the one that I know about. It takes about 4-6 weeks, I think, to receive the passports, unless you pay an expedited service fee.
As others said, I would probably go through a travel agent if I were you, since it's your first time on a cruise, especially if you go on a very long cruise.
One uncomplicated and inexpensive option to maybe consider, though, since you want a short cruise to start with, is one of the 2-3 night cruises available from Celebration; at
www.celebrationcl.com - it leaves from Port Everglades (Ft. Lauderdale) and goes to Nassau, Bahamas on 2-3 night cruises, at a low cost. Might be a good 'try it out' trip before taking a longer cruise. It will not be as elaborate and large as ships on longer cruises, but it does have a casino, spa, gym, pool, several restaurants, and most of the other amenities, and will give you a chance to see if you like cruising before committing to a longer cruise If you call and talk to them, you can probably get a 2 night cruise for around $300 total, including port fees/taxes (always check on this with cruises, since this expense is usually an 'add-on' to the quoted price), for both of you. (You always have the added expense on cruises of gratuities for your cabin steward and restaurant wait staff/maitre d').