J, unless you just like the aesthetic of a topmount, don't read too much into "disadvantages" with an undermount. Unless going with something relatively cheap and fragile like formica, with it's lack of heat resistance and being prone to staining, burns and cuts, if your top is durable and you don't sense a change of heart in 10 years, I'd not fret the undermount (and of course formica is cheap and easy to replace so sink placement is moot). But the key here is what look you want. And are you considering farm front? That can be way cool in the right application. One big regret here with our "modern" kitchen is the dual sink. We had a huge one-holer, really deep, zero-radius. Awesome. Bought it online in fact from an outfit in Vermont. Now we have two basins neither of which is all that utilitarian. But the four burners is the worst part.
Here's the sink: