I would budget between $600-900 a person to get certified.
The cost for the class and the open water checkout dives in the states run around $375 -$400. The same thing runs around $350 in San Pedro.
You can rent mask and fins in Belize but I would personally recommend you at least buy your own snorkel, mask, fins and booties if you plan on diving more in the future. Plan on around $250-300 per person for the basics I mentioned. You can go higher with more expensive masks, fins. etc. but this is a good range for an estimate.
You'll rent the BC and regulator to start then you may consider purchasing down the road depending on how serious a diver you become.
You may want to consider doing the pool and class work at home and then doing you open water dives in Belize so as not to spend a lot of vacation time studying instead of enjoying your honeymoon. Your local dive shop can give you the lowdown on this option called a referral. Equipment rentals will run around $15-20 a day for everything else you need such as BC's, regs, etc.
Check the diving link from the main page and click on the different dive ops there. The majority have prices listed for classes and dives for certified divers. Don't forget to budget for tipping your instructor and dive masters too if you feel the service warrants a tip.