It's cheaper to stay in some of the most beautiful locations than you might think, in fact everything is cheap and diving instructors can make decent pay. The best jobs, like on liveaboards to the best destinations are not easy to get into. I know 25+ year experts who spent 10+ years running PADI IDC as course director who are happy to just guide on those boats. Sometimes good photographers with good equipment can dive for free. Sometimes you can even get invited to sleep on the deck of liveaboards and eat with the paying guests if you're a good videographer.
If you're a fresh new OWSI with all of your own gear you can still find work on a beautiful island with lots of young people around partying. If you want to see amazing and rare pelagic animals you need skills, luck and probably years of wanting to see them. Different dive sites in different parts of the world require different skills to traverse. The minimum amount of training required may vary.
A lot of divers simply do the Open Water Course (18 meters max), Advanced Open Water Course (30 meters) and can then dive in the vast majority of recreational dive sites. There are also the Deep Diver Course (down to 40 meters) and Nitrox Diver Course to extend range and bottom time. Nitrox is good to have for repetitive diving (going more than once a day for days on end) in order to reduce nitrogen saturation. Some places do have a lot to see down to 40 meters, such as Coron, Palawan.
I suggest investing in training before investing in equipment. Except for the mask, get your first mask from a dive supplier and ask for help choosing one. A decent diving instructor for your first courses will make sure you have equipment that works and fits. You don't need an expensive watch-style diving computer, the big ass round ones are fine, but you should get one for the divemaster course. I use a mares computer that was really cheap and it has been working for 3 years and I just have no need for a new one.
If budget is your top concern, just go to Utila and make a deal with the owner of the cheapest shop (probably still Parrot's, what up Tatiana and Alfred) to go "zero to hero" and they will put you to work carrying tanks, assisting instructors and boat crew and even sitting in the front office. You might even get a free hostel bed out of it. Make the course slow and enjoy what may be the best weeks of your life meeting new friends and experiencing the ocean.
If you can find a deal like that (other places offer similar deals) then just leave yourself 50-100 bucks a week for everything else. Thailand is a little more expensive. The Dominican Republic is nice, especially Bayahibe but you need to speak Spanish. Apartments can be found and rented and shared and whatnot. I had a 1 bedroom furnished place in Utila for $300 US per month and my friends that I used to constantly chide because they put tobacco in the joints lived downstairs for a shared apartment for 3 of them for $200 each. I prepaid my electricity for about 10 bucks and still had some leftover after two months.
I know plenty of OWSI instructors who started diving less than two years ago making more than $2000 per month in places like Utila and Koh Tao and getting by on $.50 beers and $1.25 curry and seeing whalesharks regularly. Philippines is good too but you won't find much weed there with Duterte leading his drug war. Indonesia is even better. Cozumel and Bayahibe are easy to get to. Hawaii has a place that will use your GI Bill and include good equipment for you to keep. They see mantas all the time.
Just get your pile of shit down to a backpack and go.
