I'd agree with the 2nd choice, and if you can do herman's idea, all the better. You sound like you're pretty self directed; I bet you'll do fine with different instructors.
Regarding the equpment, the wetsuit/computer combo sounds perfect to start with. Despite what others say, there is a distinct and IMO important benefit to diving with a computer for newbies; the ascent rate alarm. The first time you get out in clear caribbean water, you'll be amazed at how quickly your depth can change; sure it's theoretically better to know the tables and not be reliant on a computer for dive planning, but the computer will help keep you from losing control over your depth without even realizing it. You could get the same benefit with a bottom timer, but as long as you're spending the money you might as well just get an inexpensive computer. The atmos 2 from scubatoys ($280) is a good deal, and I think LP has the suunto gekko for about $250, which is also a good buy. Plus, many caribbean dives are multi level, and probably everyone else in the dive group will be computer diving. As a brand new diver you'll have plenty of other issues on your mind, apart from planning multi level dives, trying to stay with a group of computer users while following your pre-set table dive plan. What if the DM decides that the group is going to stay an extra ten minutes at 60ft? For your cert dives I think you're required to use the tables for planning, but I am also sure that you can wear a computer during those dives.
Have a great time!
