Just adding on to the previous post, I usually like to switch the IE and BT around. Usually build BT first item, as it gives her a better early game advantage on the enemy ADC so out duel them or sustain them. It also allows her to become pretty much immune to poke to make up for her short range.
I also like to upgrade her W second, as really, the only benefits of upgrading e is a one less second cooldown everytime you upgrade it. Quinn's E isn't really that good to be spammed, as it does get you in to close range. It usually is used for that escape/catching up/ extra burst. Her W vision range is really strong, it is a really good ability to find people and be able to fight them in bushes.
Her Passive pretty much guarantees a free crit every 3 seconds/10 seconds. (Depending on if you hit it or not) It actually is a passive that is not very hard to control, it usually targets low hp minions, and then champions. (Usually when I hover my mouse over the champion for a long time, the passive is proced on the champion, but I'm pretty sure thats not how it works)
Quinn is a feast-famine champion, but has insane power in middle game with her ult. If you accidentally feed early game, it is very easy to catch up mid game, with her vision and ult to secure kills. However, if you don't catch up mid game (which is really hard, imo) you pretty much are screwed.
For Quinn, the best burst damage without the ult is passive,Q,AA,E,AA. Usually can be done around a second, and does insane damage whilst making the enemy unable to attack you for a while.
I also find
to be a very hard support to counter, as his e can be interrupt your e midflight, causing you to be at a lot closer range than you ever want to be. It's terrible.
I find Quinn to be really good at countering assassins and most adcs, (Basically the squishy people) However, she has a sorta hard time against tanks, and won't deal as much damage to tanks as most adcs do. (Maybe just me) If you build her botrk build instead of BT to be able to counter tanks, you will fall off late game hard. She needs the burst from her passive and Q. (I never really liked Quinn Top)