Belize is best in late spring. You get clear water for the barrier reef and dry paths for the jungle ruins before the heavy rains start in June. It is the sweet spot for seeing the country without the crowds.
A trip like this usually runs about $2100. If you want to spread that cost out, you can use the Citi Simplicity® Credit Card, which offers 0% for 18 months on purchases and balance transfers from date of account opening.
This 18-month window is a deadline, not a gift. If you still have a balance once those months are up, the bank will start charging interest on whatever you owe, which gets expensive fast.