GMail feature request

First, where should I make these requests?

Second, I'd like to be able to open my GMail without seeing all the new mail in my inbox. Very often, I open up GMail just to look up some fact that I've forgotten, or to put a date to a particular event. Seeing new mail and an unempty inbox distracts me, leading me down a rabbit hole of processing.

I guess a GreaseMonkey hack wouldn't be too hard.