I am a casual Quinn main, and i have been playing Quinn for a while since season 4, but I've only started getting serious about her in season 5. I feel like Quinn can be really strong right now, and especially top lane. Her playstyle is on of the best I have ever experienced on League, and I want her to be more recognized.
Quinn is a champ that goes from marksman in lane, to an assassin that can instaburst carries late game. There are multiple build styles on Quinn that I hope to cover in this guide that include AD offtank, assassin, and AD carry.

The general burst combo of Quinn is going to be this
Normal form auto(when the are marked usually by the passive it gives more damage)-> Vault->auto-> Blinding Assault
Ult form Vault->auto-> Blinding Assault->auto->R

Always take flash on Quinn just because it is a great summoner on most champs. I prefer Teleport on her top because if you're against a tank, you're probably going to have to roam a lot if you don't get early kills. Heal is best on ADC Quinn because she can easily win close trades with it. If you're going jungle then Smite is the way to go.

Start-Usually go Doran's Blade and Health Potion for the start, but if you're going up against a hyper tank, then it might be wise to start on a Blade of the Ruined King early on.
Core- Statikk Shiv is really a must on Quinn and i usually pick it up first especially in top. It has incredible synergy with her Harrier passive, and deals great damage, even without building any. Get Berserker's Greaves either right after Statikk Shiv, or during the build, because its actually very important to get the mark off when you Vault. Infinity Edge is also a good build on any crit marksman. Pick up an Infinity Edge right after Statikk Shiv if you're ahead, but if not get started on a selected secondary item to help counter your laner.
Choose 2-After getting a Statikk and boots (and sometimes IE) its time to think about what item you need to counter the opposing laner. I will list the item and its purpose below
Trinity Force-For tanky sustain, and the spellblade passive combos really well with E proc to increase bursty damage, and gives mixed damage against tanks.
Blade of the Ruined King-Against tanks, and gives good sustain, attack spd. If you're up against a tank, I'd advise getting this right after statikk and before finishing upgrading boots because a tank can outscale and you'll do no damage.
Maw of Malmortius-Against AP bullies or a dive comp. Also helps if you're going for a bursty path.
Youmuu's Ghostblade-Against High/Low mobility tanks. Allows for penetration, good kiting/gap closing against high mobility, and capitalizes on low mobility tanks being low mobility.
Last Whisper-Good item to pick up once a few enemies pick up armour. Usually a good choice in most builds, and a go to if you're unsure of what to build next.
Zephyr-Against high CC.
Frozen Mallet-Against high/low mobility. also good for a tanky build.
Phantom Dancer-I wouldn't recommend going PD on Quinn, just because Statikk has so much synergy with her. Also, her ult passive makes her move through targets in ult form anyways. I would only get this if i was really behind late game, and sold Statikk.
Black Cleaver-For a really tanky team or a fed tank.
Runaan's Hurricane-If you're so fed, and your team can't do anything in team fights. Also works well to apply on hit effects. People usually say this really isn't a good item on Quinn because for a portion of the game she becomes melee, but it is still a viable build.
Mercurial Scimitar-To cleanse stuff like Zed ult.
Skirmisher's Sabre - Warrior-Yes I've tried Quinn jungle. It's not as bad as it seems, because she has a blind, and extra mark damage early on.
Finishing Items-Just choose 1 finishing item, and it can be built at any time, but is recommended to be build last.
Guardian Angel-If you have quite a bit of health, so that you can add some resistances. Usually get this unless another prerequisite is met.
Bloodthirster-With high attack speed.
Randuin's Omen-Against heavy AD team. The slow can be used with Valor's dive to apply more CC if your team is lacking.
Banshee's Veil-Heavy magic damage enemy team. combos with burst because of the spellshield.

It may seem like on my recommended items for each matchup has a lot of frozen mallet, and that would be true, because the whole reason Quinn is effective is because she is ranged, and she kite can extremely well with Vault E. E will not always be up when an opponent all ins, so the extra kite works very well.

The CDR really helps with her ult cooldown even if it does;t feel like it. Going into the Spell Weaving and Blade Weaving sections is really key, because it works so well with her combos of auto-> Vault->auto-> Blinding Assault. The rest is just general AD with 9 in defense.

I use a basic set up that is found on a lot of marksmen that seems to work really well. I also like to use 1 mark of crit, because I feel like an early crit can sometimes win lane.

I have tried to cover every aspect of playing Quinn, and if you have any questions, feel free to comment. I want Quinn to become recognized and played more, and i really hope rito does not rework her like the rumors say, because her kit is so well done that i cannot get tired of her. This guide is constantly being updated whenever i find something that i had never known before, or i go up against a new match up worthy of jotting down some notes on.