Hi I'm Sokka on NA server and have used Jinx to climb through gold and into platinum. My build is very similar to most but would like to throw in some input.

Just like every adc go AD marks, Armor seals, MR glyphs, and Attack Speed quints.

When I play Jinx the goal is always get BF Sword before first time backing. If you are unable to do that get pickaxe and/or boots. Then I try to get pickaxe and BF before buying berserker greaves. Then the standard Infinity Edge is a necessity. Next depending on whether you're winning or losing you'll want to buy either Statikk Shiv or Phantom Dancer. If you're really far behind buy an Avarice blade that you will then turn into Shiv, however I almost always buy Phantom Dancer. Shiv's lower stats just don't seem worth the 300 gold discount. Bloodthirster will be the next item almost always. At this point a lot of people will buy a Last Whisper; personally, I prefer another Phantom Dancer. My reason being: this will put your Crit Chance at 90% rather than 55%. A Crit being nearly guaranteed beats out the 40% armor ignoring. If you're looking to carry you will have to do more than just kill the tanks. Therefore, buying another crit item will allow you to become surprisingly bursty and your rockets will be killing the enemies from a long distance, hitting as an AoE, and extremely effective as wave clear. Last item will usually be a defensive one. The three I pick from are: Banshee's Veil, Guardians Angel, and Mercurial Scimitar.

Q,W,E and max in that order as well.

Positioning is the hardest part of playing ADC. You're an extremely important part of the team and need to stay alive. That being said you can't rely on a support to do that. With Jinx's rockets you are able to position farther back than a normal adc. The only time I use Machine gun while team fighting is when I'm in no danger and can freely attack because the enemy nearest me is cc'd or something. Rocket AoE is also a big part of Jinx, landing a big crit rocket on 3+ members can be a deciding part of the fight. With all of this power given to Jinx she lacks in mobility. Playing passive as her is of utmost importance. When the enemy or your team engages you don't want to be a target right away. Most people will use their abilities on whoever is easiest, so if you're somewhat far away they'll probably blow their cooldowns and you'll be free to unleash hell. Another reason to play passive is because if you can stay alive during the fight long enough till an enemy you dealt damage to has been killed your passive makes it really easy to kite and snowball the fight.

Basically what makes me different than some Jinx's out there is that I build Phantom Dancer over Statikk Shiv and that I build two of them. Team fight wise, some will use machine gun more than I would, however Rockets are the better way to go 85% of the time.