I would never discourage anyone from doing what they want to do, but for just a 10 day trip, I would plan less and take it all in as it comes to you. Depending on your personality, planning the steps for a dive cert (even with major portions done stateside) can take away from just experiencing the good life Belize has to offer.
That said, boat rental is a good question. Never hurts to have leads before you arrive. I will leave that to others as I typically do a charter where I can simply sit back, snorkel, and imbibe heavily
Gone out twice with Oliver -- he is da man!!! Fish, snorkel, beach BBQ with your catch of the day -- bliss!! http://caribeantoursbelize.com/
Just my opinion, of course. I planned far too much my first trip and wished I had just come to town with an openness to explore as the mood and conversations with locals dictated.
As for daily budget, I echo colly, but it depends a lot on your tastes and what "moderately" means. I typically do one swanky dinner per trip and that $100 is gone right away. For most days, for two of us, I'd say we spent closer to $150 for meals and drinks. You can do it for much less (and we have when we needed to), but that $150 includes a potential desire to catch the Coastal Xpress or a cab to a more remote location for a drink, or buy a round of shots for new friends.
Best advice I ever got is to pack and when we thought we were done, double the cash and get rid of half the clothes. That was amazingly accurate