Even if your flight is on time, you're arrivng pretty late in the afternoon. There's a Tropic flight I think at 5 p.m., but seems like the Maya Island flight is at 4 or a little after, so it's going to be tight getting to Placencia, what with potential flight delays and getting through customs.
I'd suggest that you do make reservations, with Tropic, so at least the airline knows you are coming, but if your flight is late you may have to make other plans. Fare is arouned US$65 one-way.
Depending on which route you take, it's over 100 miles and three-to-four hours plus by car (and it can take twice as long in bad weather). I don't recommend you drive it after dark. By bus you have to change in either Belmopan or Dangriga, so it's considerably longer. As I recall there are no late afternoon buses to Placencia.
There are quite a few budget/moderate places in Placencia village and a few such places north of there. My top picks in the village would include Tradewinds, Seaspray, Harry's, Ranguana and Coconut Cottage. If you don't need to be right on the beach, Deb & Dave's and Barracuda & Jaguar Inn or Lydia's are good. North of the village low moderate places on the water include Maya Playa and Xcape.
Belize First http://www.turq.com/belizefirst/