There is alot that no one will have, but which way do you want to go.
A small, light, fast caliber for range shooting and varmints?
A big, heavy, slow caliber for hitting hard? (Or, for 1,000+ yard gong shooting, if the Wind is just right

)
A 336, but more so, like the AI you mentioned.
Then, how do you want it equiped? Synthetic stock? Perhaps some unique wood finish? Bobbed barrell?
Tacti-cool stuff? Scope? Sights? Retro (cowboy) equipment?
Do you want it specialized for some particular task?
Lots of questions.
I've lately been thinking that a 6.5 levergun would be cool. You would probably be limited to a two-shooter, though. Not that I can afford it.