And to explain PUP/THF... it's for one reason, and one reason only. Treasure Hunter. /THF is a situational subjob for when you're willing to sacrifice combat benefits from more standard choices like /WAR (better offense), /NIN (shadows for defense), or /DNC (variety of benefits, particularly Waltzes), in exchange for the Treasure Hunter II trait from /THF to increase item drops. You'd still play PUP like normal though and use a Hand-to-Hand weapon since it's your best weapon for killing quickly and actually taking advantage of TH.
Probably the most significant situation where a PUP might go /THF is Dynamis to farm more currency, particularly solo. A few specific reasons this works well:
1) A mage puppet alone can keep you alive fine in Dyna if you know what you're doing, so using /DNC or /NIN to survive isn't necessary.
2) Over a 2 hour Dynamis run, the overall benefit from Treasure Hunter increasing the average currency drops per mob outweighs the faster kills (for less total currency) you could accomplish as /WAR.
3) Unlike some jobs, PUP doesn't have to rely on Job Abilities for procs (triggering a random weakness to cause better drops) on Dynamis mobs, since Automaton abilities like Strobe, Flashbulb, and Disruptor count as WS procs. That means that unlike many jobs, /DNC isn't a practical necessity for currency farming and PUP can instead target the mobs that are weak to WS procs. And since many other Dynamis farmers (for instance, the many BST/DNC) will leave those WS proc mobs alone, you can avoid some competition and potentially increase your amount of kills during a run since you aren't fighting over mobs with other players.
So to sum it up again, unless you're really after increasing drop rates with Treasure Hunter there's no good reason to be using /THF. Definitely not something you'd want in a typical party or group event.
Anza: Titan 2004-2011 / Capuchin: Phoenix 2011-???