Whatever feels comfortable to you. Probably to your chin since that's what you did seated. If you have your "shoulder shelf" going on with your lats flared then you probably won't be able to bring the bar all the way down to your chest anyway.
Second question, are you talking about push presses? If so, I like them but prefer to do strict military presses. I'm weak as a kitten and tiny so take my thoughts accordingly.
http://www.youtube.com/watch?v=xLcntfkyXbM This may help you with the terminology. The video calls the military press a shoulder press. Doesn't matter. As long as it's strict, meaning there's no leg drive at all. CT also makes a distinction between push presses with a hard leg drive (I believe he sometimes refers to these as jerks) and push presses with only a slight drive just to get the bar moving.
Do whatever works best.