I don't know exactly what to expect from Abrams, since my only exposure to his stuff was seeing maybe the last 10 minutes of one of the MI movies on TV once. The one with the tunnel helicopter explosion.
I doubt we're getting "The Trouble with Tribbles" though. I mean, for a lot of people that is the defining episode of the series. It's one of those episodes (there were a bunch of them) that ends in a sort of bizarre 'bridge komedy' routine. I bet Abrams sat down with his list of popular TOS episodes and the first one on the list has Kirk getting buried in little hairy balls.
Abrams is more of a TWOK fan, so I imagine his movie will be more in that tone: Big villains, lots of character history getting dredged up, space battles galore, maybe some minor message in the same vein as the age/revenge thing.