I couldn't see going with LOTR or TSPP as an only game. Both are great but you would never be able to play multiplayer on them and you'd have to set aside at least 30 minutes every time you play a game. Maybe if you were allowed to keep 2-3 pins.
I'd have to go with something with medium range depth. Probably STTNG or TZ? ACDC would also foot the bill. Out of those 3 I'd probably go with STTNG. The game has great flow, is always challenging, and is just a complete package. It's the longest lasting pin in my collection for good reason!