Um, I think just looking for a specific stat to profile a player is a bit flawed because the decisions you will face at the table may be clarified with the use of different stats for different situations.

However, I think the standard VPIP/PFR/AF gives a pretty good indicator on the players style, generally giving away info such as tight/looseness and also how aggressive they are (do they like to raise preflop? do they like to splash chips around postflop? are the a calling station? etc..). All these sorts of things can be interpreted with the basic stats.

To understand more about how positionally aware an opponent is, the attempt to steal blinds stat, (ATS or ATSB) is a very good indicator of this.
If someone never steals, their opening range isn't deviating much from their UTG opening vs their BUTTON opening. However, if someones ATS is high, typically their button opening range is much wider than their UTG opening range.

I think C-bet sats are pretty key as well when it comes down to estimating your EV of the options you have in postlfop play.