Car rental are expensive. Not advisable.
Tropic or Maya airlines fly from Belize International or Belize Municipal Airports
BI to Placencia....US$75
MA ....US$55
Approx.
The bus does take a lot longer but for a first timer you get a lot of bang for your buck. You get to see things that you would never see flying.
Try Serenade Guest House in the village for low / medium cost accomodations.
They are on the sidewalk overlooking the caribbean and are very hospitable.
Good Luck