The one that's most comfortable for you to play - which, with Les Pauls, generally means very very comfortable indeed
I know people who can afford anything they want who've sold R9s in favor of goodwood era les paul studios, and guys who are unemployed who play a norlin era modded deluxes - the actual model of the les paul is almost completely irrelevant unless you want to keep it completely stock. And in that case, you would be better off with an ESP or something that, stock, has pickups closer to the genres you want to play.
The real question is what pickups are you going to put in the Les Paul you are most comfortable playing? Because they're all the same except for the neck varying from 50s to 60s and the axcess as chris mentioned
Because even if it was the greeny or adam jones, you'd probably have better results for thrash with aftermarket pickups honestly.
I would start trying out les pauls at the closest guitar center paying attention to specs - as in neck carve style, etc
Then after you have a better idea of what you jive with best, THEN start doing research on the models that have those specs