For me, there's a difference between most-picked and best. I'm not gonna vote formally but bifurcate the two with reasons.
In terms of most picked, I'd have to say Shottyman, Dodgemaster, and Badass (in that order), if only because a lot of my builds that have significant trees are shotty ones. MFa is a pretty flexible master trait if your primary is still shotguns, and MAD is far more shotty-centric but with a huge bonus for it. By contrast, my rapid-fire builds are usually Fin/SoaB/EE without going for any master trait (with the occasional exception of MAc, which means TH and WK) and my pistol build just adds SoaG first. Other than that, the shotty/explosives hybrid only needs Juggler but WK is a backup. Overall, the shotty-based advanced traits have a much greater synergies than the others. (DG is an exception, but that's not for this thread.)
In terms of best (that is, biggest benefit potential) I'd have to mark Intuition, Dualgunner, then a tossup between Whizkid and Shottyman (in that order). Intuition (at both levels) is quite useful, but monster location gives the player an unparalleled advantage. Dualgunner increases your pistol DPS output by ~75% and lowers the necessity to reload in a tight spot. Whizkid modding can be a huge benefit (P3 combat shotgun is godlike) and releases a huge potential out of weapons (like B3 BFG or P2T3/P3T2 pistol); with assemblies it's even more flexible. Shottyman is free reloading each step, allowing the player to make use out of dodging, hit-and-run, or whatever is necessary.
This isn't taking into account the traits that come before it, mind you. The synergy of basic-advanced traits is just as important as advanced-master ones.