I am a Plat 5 player but I have climbed up the ladder from bronze 2 using Quinn in the jungle, top, and mid. There are some misconceptions about Quinn that I would like to share with you. First, She is a god-awful ADC and should never be played there. Second, She is better as an assassin than a marksman. I have played over 60 games on her in ranked and have over a 60% win rate so I think I know what I'm am talking about when it comes to her best play style.

I run two life steal quints as you are a "marksman" so you are squishy as all hell. You'll need to be able to sustain a tad bit in the jungle so I recommend two life steal quints. Then, One AD Quint and AD marks for obvious reasons. Next run flat Armor and Scaling MR Seals and Glyphs as you want to be able to roll from levels 1-9 but be able to survive late AP casters Damage.

Just go standard Ad Jungle Masteries.

You are going to want to get stalker's blade as you want to be able to slow any Champion that you want to kill. You'll want the warrior enchantment as it will give you some early damage with the AD and Armor Penetration. Also, The CDR is really good on Quinn as her ult has like a 5 year cool down. Next get Ninja Tabi for sustaining so Auto Attack Damage. Get BORK right after that as it is the most key item on Quinn. Next, you want to get black cleaver as that **** is really good with quinn as it gives that muck needed CDR plus the passive is good for shredding tanks. After the you are going to want to get Shiv as it will give you that elusive crit chance and attack speed so your split push will kick the enemy team's ***. Finally, The sixth item is a judgement call. If they are focusing you then buy that GA and save yourself. If you are flying all over them then you buy either a Maw or a Last Whisper. Either way, if you are hitting six items early then you prob going to win.

Start with E as you will want to invade the other jungler with your team at level 1. You can use the harrier Auto Attack, E, Harrier Auto Attack to shred 200 hp from a single target so invading is easy. If you have a other laners with good CC level one then you should have easy first blood. Take Q level 2, W level 3, then max Q, then E, then Ult, then W.

Honestly, Quinn is a great assassin with high mobility and burst potential. If you are feeding (which can happen), just play like an ADC. Stay in the back and don't take to much damage. If you are rolling then play like a zed where you go in on their easiest target and kill them with ease.
Pro's:

Has high burst potential and can kill other ADC's with ease
High mobility so she can gank lanes really easy.
Can have lane pressure before level 6 (Unlike Warwick)
Can Split push with ease.
Can take objectives pretty quickly

Con's:

Squishy
Not very effective if behind
Against a tanky team Quinn wont do ****.