Royal Caribbean hands down. There are only two ships that sail from Port Canaveral to the Bahamas other than disney and that is Carnival Cruise Line and Royal Caribbean - You'll find I'm very bias as I have sailed 12x's with RCCL and only 1x with Carnival - that is no coincidence that is how bad of a time I had on their ship.
RCCL's Sovereign of the Seas - runs 3 night and 4 night cruises to the Bahamas. The three night cruises sail Friday through Monday and the 4 night cruises sail Monday through Friday - I have been on this ship personally 3 times. The Sovereign just came out of dry dock in November '04 after being completly refurbished and updated - it now boasts a rock climbing wall, Johnny Rocket's 50's style restaurant, sorrento's Pizza, Seattle's Best Coffee, a large casino, 2 pools and a wonderful spa. The prices start around $300 and go up the more you get into spring break season and summer.
My personal reasons for cruising with RCCL is that they are a very moral cruise line - what I mean by that, is that they have all the fun (bars, clubs, etc.) of a similar cruise line (Carnival) but they do not offer things like topless decks or scantilly clad showgirls on stage - Their shows are amazing more theater than Vegas - very entertaining even for people like my husband who could give a rip about theater - he loved the shows!
Also there is no comparing the food at RCCL and Carnival - RCCL wins awards every year while Carnival sends home guests with food poisening (no joke that really happend)
Now, in all fairness Carnival is not a bad cruiseline - they are just known as the less of the two - and as far as price - RCCL beats them every time with the smaller ships. RCCL's larger ships are much more expensive than Carnival's as they are nearly twice as big as Carnival's largest ship - and in the cruising world, larger is much better.
The larger the ship - the more stable (i.e. less sea sickness) and the larger the ship - the more activities and more things for you to get your money's worth!
The Sovereign of the seas is 880' holding 2,852 passengers (double occupancy) The rooms range from least expensive being an interior no window (but a nice mirror

) up to a ocean view (nice window, no balcony) then up to the balcony rooms (wonderful to wake up to and eat your breakfast on!)
This is one of the smaller vessels that Royal Caribbean has - although now that it's made it though the refurbishment - you'd never know it - it is quite beautiful!
Ok, On to carnival.
The Carnival ship sailing out of Port Canaveral is the Fantasy. The Fantasy is a 15 year old ship that has yet to be refurb'd and needs it badly - frankly they need to retire this ship altogether as she gives Carnival a bad name - Carnival has several newer ships that are quite nice but as far as your money's worth - I'd stick to RCCL anyday.
There are no 3 day cruises that sail to the caribbean - the closest is a 4 night out of Ft. Lauderdale - and it will jump to approx $700 per person for the cruise,
I always recommend the bahamas for a first time cruise to get out there and see if you like it - the bahamas are close enough to land that you never really hit rough seas so it really gives people the chance to see what cruising is all about.
However, once you've cruised once (you'll be likely to book your second cruise while on board - that's how fun they are) You'll want to jump to a 7 nighter and try out one of the Mega Ships - largest ship on the water next to the Queen Mary and even she will lose that title back to RCCL in May of '06 when their newest ship comes to America the Freedom of the Seas - can't wait to get on her!
Anyway - if you have any other questions please ask away!