It's a really tough topic and what applies to one, doesn't to someone else, and varies between what type of music your creating, and even the end result, how it's mastered.
I've found with some songs I've gone overboard on silencing the background, it's changed the whole feel, and not for the better. Other tracks are woeful with background noise left in. But in general, I manually do all the vocal tracks. Complete silence where required such as a lead break, and usually somewhere between 6 and 18db down between vocal lines, splitting and fading in and out if necessary. I always leave traces of everything that's related to 'vocal' noise. I've tried automation, but get much better results going painstakingly slow between each vocal line. Takes ages but it pays off. I tend to use automation on guitars and gates on the bass, but the more work I do, the better I get at the recording stage, getting rid of most unwanted stuff before it hits the disk.
Ears before eyes as someone else said. Same with Melodyne. Very easy to group notes, bars, or entire clips, for processing. But you cannot beat manually listening to, and modifying accordingly, each and every note.
Depends on how much time you have I guess, and what level you are prepared to settle for.
regards