To update you all on my caulking adventure!!! It looks pretty darned good for my first try. It definitely has a few places where the caulk bunched up when I pulled the tape off (I think I waited too long....it started to harden faster than I anticipated). But, nothing a razor blade can't cure!
I definitely need to get my butt in gear and give my grout a good cleaning though! Any tips on good products for this besides the obvious (bleach)?