Most people just hop a bus to Playa and take ADO from there (the newer bus station) to Chetumal.
You can save yourself 25 bucks or so at Chetumal by just busing over the border rather than taking a taxi, and it's almost as fast (assuming your connections are okay in Chetumal).
As to hotels, in Chetumal it's hard to go wrong with Los Cocos. In Corozal, Nestor's (now called Las Palmas) is fine, but Hok'ol K'in for the same money (around US$40--$50) is on the water, with a nice view and a nice breeze. At the South End, Tony's, Corozal Bay Inn and Copa Banana are all excellent. Corozal Bay Inn is the nicest, but a little more expensive, around US$80.
Corozal is inexpensive compared with San Pedro, but Chetumal, even though it's a real city with all kinds of supermarkets and stores, a mall, movie theaters, etc. is less expensive than Corozal.
Just realized you're arriving in the late afternoon. That means at best you'll get to Chetumal very late and will probably want to overnight there, as there are no buses to Belize in the middle of the night.
Both Tropic and Maya Island each have around five flights a day from Coro to San Pedro. About the same price, same service, similar equipment, similar safety record. Just whichever is flying when you want to go.