Max w first. Sounds stupid considering q has better single target damage, but w gives you relatively safe harass and wave clear, wave clear being the most important thing, as being pushed under turret is the natural way to stop an assassin from roaming.
And I always found athene's to be a good first item majority of the time. Build fiendish codex on first b, build into athene's if normal laning, dfg if way ahead. Followed by either dfg if they built mr, or deathcap if they didn't.
Also, get used to using weird spell combos when you get ult. If I hit 6 first, my standard combo is q(w) > w(q) > e > r > q, as the 2 or so second root is lethal. It's really important to know the damage limits so you know what will work. Q and e forms of r deal the most damage, but w form of r is good for catching people off guard with your gap close distance, as w > r can basically cover 1/2 of distance between midlane turrets.
There's a lot about her you really only learn by playing her, namely because she's a heavy outplay champion.