I won't try to re-tread everything, but:
1. Gott's for lunch and Press for dinner are great recommendations above. Farmstead, Goose & Gander, Brasswood, and Market are all great. Mustard's is fine, as is Brix next door.
2. I really prefer the small production places and that's basically the only ones we go to anymore, but they are harder to get into without knowing people, and the etiquette (and the wineries' economics) are going to require that you purchase a decent $$$$ amount in return for them taking the time and pouring expensive wine.
With this being your first trip, the recommendations for the larger places are fine so you can get a feel for what you like. But try to check out something a little smaller -- I would suggest somewhere like Krupp -- much smaller production than most of those listed (they do 3000-3500 cases), and the people are very nice and accessible.
I would also recommend Chappellet (mid-sized production) just because they have a great view of the Valley, and it's a pretty drive up there. It's as good of a view as Sterling but better wine.
You can also probably get into Revana, which has nice cabs and is also not a place that over-produces