I'm renovating a bathroom and plan on using granite counters. I want the
keep the depth of the vanity to a minimum to keep a reasonable space in
front of it, preferably 18-19" but probably need to go more to fit a
reasonable size sink. I'm building the vanity so I can make it any size but
I'm not sure how to determine it.

I went to a granite company today but that conversation left my more
confused on how big I need to make it. He seemed reluctant to make any kind
of recommendation other then "bigger." I also tried the Home Depot, but got
nowhere there.

My question is, how much clearance do you need to leave at the back and
front of the sink. For example, I'm looking at at rectangular Kohler that
has an outside dim of 14 1/4" front to back (12" opening). How big would by
vanity need to be?

Lessee, 14.25 undermount sink, at _least_ 2 inches for the fixture,
depending on the user interface, plus some buffer for the mounting
hardware, let's say 3 inches, your overhang(3/4 inch), and room for
the undermount to clear the vanity (1/2), plus the thickness of your
vanity carcass I'd say 20 inches for your top. So 19.25 inches for the
vanity depth. I think. Tom