Bredman,
I think we've got similar styles. The only time I ever plan on purchasing or traveling with much gear is when I do the inevitable divemaster internship... because they want you to have your own gear. There are places that will provide gear - it'll cost you more of course, but not as much as buying the gear would.
Rental gear doesn't bother me or my girlfriend, at $0 - $15/day to rent it we have years to go before we "could have had our own gear".
If I were you, I would buy a computer for sure, that's a must, and maybe your reg/octo/spg. Mask, reg, octo, spg, 1st stage, and comp won't be cumbersome in your pack at all. In the Bay Islands getting some sufficient fins/BC/wetsuit shouldn't be difficult or expensive. Then sell them when you leave. Buying, & subsequently selling, cheap used gear would be more difficult in Playa del Carmen or Bocas del Toro. Easy in Cozumel, easy on Ambergris Caye, more difficult in Tulum or Caye Caulker.
I've been to most of the good backpacker dive spots in Central America - the notable exceptions being the Bay Islands, and the Corn Islands. I would say there's a %95 chance I'll do my DM in Roatan or Utila if I don't do it in Asia, it has the best combo of amenities, there's a reason Roatan & Utila pump out DM's & Instructors at such a furious place.
The diving in Playas del Coco is very good, the town is blah at best (and my standards are low! I was anything but charmed).
Bocas del Toro is loads of fun, great town, the diving is blah at best.
Caye Caulker is awesome, cheap and great diving, but island fever is a real concern when not diving - "laid back" is a double edged sword...
Ambergris Caye is great. San Pedro has a little piece of my heart, but it also has some of my wallet if you catch my drift. Worth considering for sure - the higher price tag is justified.
In Cozumel food & lodging is surprisingly cheap, regular diving is spendy but DM class isn't. Charming place with great people. The diving is fantastic. Cenotes are right next door, as is the modern world (has its advantages). Point is, don't rule it out because it seems expensive, a little money goes a long way there.
Nicaragua is dirt cheap, people are really nice, the Corns are a long way from everything and as such the price tag goes up, and you can't jaunt to somewhere else in a couple hours.
Costa Rica is fun, Tamarindo will have more going on that Playas del Coco, especially if you want to surf. Great diving, pretty cheap, CR is a weird place though... just has an odd vibe altogether.
Honduras is really enticing to me, islands, coast, & inland. Honduras, Guatemala, & Nicaragua are back a few decades from their neighbors - to me that makes them substantially more interesting and fun. Mega cheap.
Good luck,
I'm on the other end from you, I'm trying to figure out my Asia itinerary. If I can be of any help to you just let me know.