There are several areas where there are a good concentration of dive sites and dive shops/resorts in the Philippines.
I have not been to most of them but can offer some suggestions based on my experiences.
Bohol, the diving is centered around Anola Beach on Pangalou Island in the south part of the Island. The beach itself is starting to become a party spot, especially at night but there is a lot of good dive sites and some pretty cheap places to stay. You can fly into Cebu, then take the ferry for about 500 p. I dove with Philippine Fun Divers there and they were great. Lots of dive shops not necessary associated with a resort so you can split the accommodation and the diving. This may get you a better overall price because dive resorts tend to be more for the tourist's with bigger budgets.
Diving there is all boat dives, lots of good beginner level dives. Well worth a look.
Dumaguete, mostly just south of the city, the diving there is a mixture of shore and boat dives. The beach is very rocky and some entries pretty difficult. The dive operations are mostly affiliated with a resort so the usual practice is to stay where you dive. Diving a little moire pricey than Anola Island. Easy to get to, take a bus from Cebu to Dumaguete then a local transport to wherever you are staying.
Cebu itself, some diving right from the city, I took my Rescue course there, not the best diving but I was only there a couple days so it might have been timing. Many options for accommodations and dive operations. I dove with an independent operator who was affiliated with a beach place that catered to independent divers. Up side was the training was pretty cheap but I got what I paid for I was very unhappy with the training.
Puerto Galera, I am there now but have not dived due to nasty head cold. This is a major party spot and teh town of Sabang is fill of professional women, who don't have an office if you know what I mean.
Next month I am going to Moalboal, again easy to get to from Cebu, independent dive operations appear t0 be the norm, some published diving rates the lowest I have seen.
Places I have looked at on line but not been to for diving include the resort destinations like Coron (expensive to get to and accommodations are pricey) Subic, and places like Boracay etc appear to be more pricey.
I'd take a good hard look at Moalboal and Anola as I think they meet your needs better, easy and cheap to get to, and with dive shops independent of accommodations offer more options.
Also check out Airbnb as you can get self contained accommodations which give you the option of self catering.
Remember when you buy a course, you are not buying an agency, you are picking an instructor. As far as I can determine all agency training is pretty much the same and they all rely on the actual instructor to deliver so the instructor is more importance than the agency.
Don't shop only on price, i made that mistake on my rescue course and am not seriously thinking of re-taking with a different instructor/agency.
Good luck and welcome to the wonderful underwater world.