Quagsire... I would prefer Wooper (one of my all time favorite pokemon). I just love the way it looks and it's goofy and oblivious nature. (In a funny way not like the Slowpoke,king,bro trio).
Anyway... This would have been a very bulky pokemon if some stat investment have been made... But still it is pretty good!
Major let down is it's stats... But who cares, it has very good abilities, good enough movepool and only one weakness to grass.
It's easy choosing it's ability... Damp is not to consider as explosion is rarely seen nowadays. So If you have a quagsire make sure it has the Water absorb ability. If you don't have a Quagsire, go to the dream world and catch an Unaware one.
Speaking about physical offence, it's usable moves are low... It doesn't have anything besides Earthquake, waterfall and Dive that are stabbed. It's other decent options include Return, Brick break, Stone edge and rock slide. (It's 4th generation had more options with Ice punch, Focus punch, and Aqua tail).
It has also decent disruptive, supporting, statusing moves...
This is my Quagsire's set!
Ability: Water absorb / Unaware
Nature: Relaxed / Impish
EVS: 252 DEF/ 252 ATT/ 4 HP
-Waterfall / Stone edge
Easy set to take advantage from your bulk... Earthquake and Waterfall are your main Stabbed moves... Recover is for healing and yawn is to force switching! Stone edge is if you want more coverage but all in all waterfall is stronger (Considering STAB) and more accurate.
Ability: Water absorb
Same as above.
-Earthquake / Waterfall
-Yawn / Amnesia
-Encore / Recover
Gimmick set but might work. Choose earthquake or waterfall so you won't be taunt bait. Yawn forces switches and abuse entry hazards but Amnesia raises your special defense. The main focus of this set is Encore/Haze... Destroy opponents that choose to set up on you... when they set up encore the move until it's useless... Haze is for baton passers or to play with your opponent's mind hazing when they think you encored the wrong set up like Curse or Barrier that makes the opponent's DEF stat go up! Recover is there if you didn't breed your Quagsire for encore. It is always handy. On this set you should not have unaware as ability so your opponent can set up!
Quagsire is best under trick room it will outrun nearly everything that isn't using priority.