This is a complex set of questions to answer. Laws vary from state to state, so take everything I'm about to say with a grain of salt.
If you are not a restaurant (your primary business is food) you cannot serve alcohol if minors are present unless they are in a completely separate area, and no alcohol is allowed to enter that area. (I've seen clubs like this).
Beer, wine, and hard liquor all require separate types of licenses. You don't need separate licenses (I don't think), but the license you get will specify exactly what you are and are not allowed to serve, and the restrictions on quantity, times, and alcohol content of the drinks.
And now my standard demographic rant :
IMO, if you can get a liquor license, get it, build a LAN for 21+ ONLY, and
never look back. Targeting the younger crowd is all well and good, but it is not (IMO) the optimal idea. The age of the average gamer is 35+. Serve alcohol, target an age range of 21-40 (at least). Don't serve alcohol, and you miss out on that potential income (markup on booze is HUGE), and only gain the sales to 12-20 yr olds.
For inspiration look at the
Mana Bar and
Barcade