Well, I assume those 12X12 are fairly thin, and therefor, regardless of the the sink set up, the tiles need to be well supported underneath. I would think you need a countertop of 3/4" plywood, with 1/4" or 3/8" cement board on top of that. Now your granite tiles will be well supported, and- there should be no issue of the sink laying on top.
A drop in sink should have a good bead of silicone applied UNDER the lip as it is set down in place. Any silicone which squeezes out should be immediately cleaned up, leaving only the tiniest caulk joint. This creates a very clean appearance, and is easy to keep clean. With 100% silicone, you need to use denatured alcohol, not water, for the cleanup.
Now, note that we have created a countertop with a total thickness approaching 1½". This will be an issue for the faucet shanks . You need to plan in advance. Some faucets have extra long shanks, some manufacuterers have extension shanks available....just figure this out in advance. Don't wait until you have the whole clan coming tomorrow for thanksgiving dinner, to find out you can't install that foo-foo designer faucet you fell in love with!