Hi Cotton, we just relocated in March and were having a hard time finding a place. May should be better of course as season will be over.
We are ever so grateful to Keith who runs B-leases as he found us an amazing place in the area we wanted

He's been a great help. You can find his email address in the accomodations section of this site and his his phone number here is 011-501-226-2186.
As for money, I would just have it deposited in your account at home and use your debit card down here. I think we pay a $5 charge so its much cheaper than wiring fees. You just go in to the bank and the teller does it all for you. I think the max per withdrawl is $3000 Belize per day.