Since you haven't done warm water yet almost anyplace will look good. Another question is, since you are in Vancouver, are you thinking Pacific or Carribean? From Vancouver, maybe you should look at Hawaii. With 2-3 weeks it's well worth doing more than one island and there's tons to see above water as well. I'd suggest Maui and the Big Island. You won't see a lot of the colorful corals like other tropical places, but lots of other good stuff, and likely big stuff. In the winter the water won't be quite as warm as some places, but will still feel warm to you.
So many great places to go elsewhere in the Pacific, though most probably longer or more expensive to get to than the Carribean even from Vancouver. And doing your first trip there could spoil you for the Carribean. Any of the popular places in the Carribean are a good bet for a first warm water trip, though even they have their own version of "winter" weather. Might come down to which gets you the most reasonable flights ($ and time.)
Cayman is always good. On GC I would also suggest staying at Cobalt Coast, though in the winter Divetech will often get blown out of the more desirable northern sites and shore diving directly from the hotel is less likely (though they've got another place to shore dive nearby that is sheltered.) Or check out Little Cayman (again, you could run into a winter stretch where they have trouble getting around the island to Bloody Bay wall some days but it wouldn't stop me from going.) Turks & Caicos is a good place to do sometime, main islands would be Provo or Grand Turk which are quite different. Bonaire is always a good bet, but can be a pain to get to even from the east coast. Curacao is good too with similar diving (if you go to the right places) but unlike Bonaire not all hotels are dive oriented so you don't want to stay just anyplace there. Belize is good but I think the best stuff is accessed mostly from liveaboard. Roatan and Cozumel are popular. None of these places have a lot of wrecks, usually a couple at most and some of those don't look much like wrecks anymore. For more wrecks could look at Bermuda, Aruba, BVI, though the reef diving may not be as good in those places esp. Bermuda and I don't know that they're worth the trip from Vancouver for diving. If you are really into wrecks I'd figure on going to Truk someday.
There's a bunch of other Carribean islands that aren't as popular as dive destinations but still have worthwhile diving. They're not as popular because of some combo of hard to get to, not quite as good diving as the big names, fewer good dive sites, less choice in dive operators or hotels, or in some cases simply lousy marketing. I'd probably start with one of the "usual suspects."
