Hey, I'm picking up Vi because, as a jungle main, I've been putting it off forever and she's been pretty consistently strong since her inception.
How do you guys like to play her? What's your skill order? What's your favorite build? How about best combos with her kit? Any unusual things you like to run with her?
Thanks for the advice! 
Punch first, ask questions while punching
First, it's false to say she was pretty strong since her conception. Season 4 was a pain for her (mainly because early gankers were more rewarded)
W-E-Q-Q-Q-R
Max Q for ganking (make sure to land it doe) Max E for clearing W last max wonder (the first point is for the AA buff to help the first few camps)
Fav build : Adapt to the game. good items are : Warrior enchant, Randuin's, TriForce, Aegis/Banshee
Best combos :
Unusual thing : Black cleaver when I'm too much ahead to care about the game.
Start W, then E, but max Q first. Then you can max W or E, you choose. She can solo dragon at an early lvl, not sure JUST how early though. I build Warrior Enchantment on Stalker's, then go full tank. However, when we are winning big time I build 1-2 more damage items :). Example tank build:
(this is against a mostly AD team, last item can easily be exchanged for MR or some offensive item).
ALWAYS gank when Vi's ult is up, otherwise you are wasting time, there is no other way to put it. Vi's ult is practically a death sentence, so use it as much as possible.
Just a tip for early clearing, remember her E resets her AA, use it wisely :)
I prefer to start w, although an e start is fine. E would be your second skill with q the final skill. Although you should max q first then either e or w, both would be fine. Her combo would be a fully charged q, auto attack, e, ult. The reason why you need the auto attack is to get the three, and proc your w and reduce their armor for your ult.
One tip is to try your best to save your ult for after your target uses flash or their escape. Another is to use E to cancel AA. Her third punch on a target causes a long animation due to her W proccing. Hit e immediately after that third hit to rush the animation. Also with regard to her E: the range is a little longer than regular AA so if your target is just out of range try to use E first.
Max Q first W second
If you get fed early buy phage and brutalizer after warrior - if you don't get fed just go tanky after warrior, her base damage is pretty high even if you go tanky
