Hearthpwn

do you guys go face with the stealth jungle panther when the board is empty or do you wait for opponent to drop a minion and trade?

Assuming you're playing a moderately aggressive hunter deck, which is most of them, always hit face if the board is empty. Revealing it from stealth only opens you up to weapons, which is fine because they take 4, and targeted stuff which actually isn't that common in a lot of decks.

Really just Frostbolt, Backstab/Evis, and Lesser Jasper/Amethyst Spellstone.

Generally wait to trade. But there are certainly exceptions.

If you have other minions in addition to the panther and expecting a clear then you might as well get some value from it.  Similarly, if you put your opponent on not having any removal then it can be a good move to break stealth in exchange for 4 additional damage with minimal risk.

And of course if you're setting up lethal then face is the place. 

this is an individual choice depending on your deck, the matchup and the resources available to each player

Depends on the deck and the situation.  In spell hunter, I tend to be a bit more patient unless I feel like I need to apply the extra pressure.