Enjoy your trip. I lived in Cebu before, and I’m a PADI instructor, so please feel free to message me. You’re right, it’s usually cheaper to land in Manila first. And yes, Manila isn’t a good airport.
Transferring between terminals isn’t easy and can involve needing to take a taxi or a Grab. Terminal 3 is the newest and nicest, but is often over crowded. Cebu Pacific uses Terminal 3, which makes transfers easier from an international flight. I have taken a free shuttle from Terminal 1 to Terminal 2 (Philippine Airlines and Air Asia). The shuttle is a little hard to find. I’m not sure if the shuttle is still running. Terminal 1, which houses many foreign airlines, isn’t easy to transfer to. I usually take a Grab.
If you want to spend the night in Manila, Makati isn’t that far if the traffic isn’t bad, depending on when you arrive. You could also walk from Terminal 3 to several hotels in Resorts World using the sky bridge. I’ve done it often. By the way, where in Cebu do you plan to dive?