Cooper,
Welcome aboard. I think you have missed the opportunity for this year by quite a large margin. Toronto to anywhere warm is long haul and would need to be planned pretty carefully.
In short you have 3 options, none great.
1- Down the Great Circle Loop - Chicago South on the Mississippi, etc into the Gulf of Mexico. There is a Great Circle organization with lots of online info.
2- Erie Canal past NYC and then down the inter-coastal waterway. Sort of the Great Circle in reverse. Same online resources as above but in reverse order. This is likely your best option.
3- To go down the St Lawrence, around Nova Scotia (but not Cape Breton) then a slow windward slog to the US and eventually down the ICW.
That said, I hear your desire to get someplace warm and tool around on a sailboat. There are many other options. Just fly and buy a boat there.
If I may suggest the Bahamas have good relatively easy sailing conditions. You could buy a boat in the Bahamas or Flordia to Georgia, or anywhere to North Carolina. The ICW is relatively benign but a lot of motoring. The toughest part is the 90-100 miles across the Gulf Stream from Florida to the Bahamas. But if you have time and patience to wait for decent weather this need not be onerous. I like Vero Beach as a staging point but others exist.
We found the Bahamas pleasant. Two major cruising grounds are the Sea of Abaco and Georgetown in the Exumas. We preferred the former. The Family Islands, any of the islands you never heard of, are very friendly and quite safe and peaceful. Not a lot of resources, but close enough to resources to not be a problem.
Many here have far more experience with the Bahamas than I. I strongly suspect you will be warned off Jamaica for many very good reasons.