you are going to have to go with Ales for sure. Lagers would take too long.
For quick turn-around, keep things lower in alcohol so that the fermentation can finish faster. Right around the 4.5% range is probably good.
The more complex the recipe (ie; the more flavors in it) the longer it will take to mellow out and "gel", so keep things simple.
If I was held at gunpoint and asked what types of beers I could produce and have ready to drink in a short amount of time, I would say
Engligh Brown/Mild Ale
Pale Ale
Light-weight Porter
Just stay away from HEAVY beers (stouts, IPAs, Imperial Whatevers, Heavy Scottish Ales, etc).
My $0.02
-walker