1. What's the best starting skill?
q if you're going to a sidelane or if there's any chance of a level 1 fight. if you're going mid for whatever reason e might be better since you can actually land it.
2. What ability do I prioritize?
e; it's easy-to-land aoe damage and the slow increases with level too.
3. What are some good items?
lots of ap (deathcap etc.) and a void staff the opponents are getting mr (which they should be but y'know). soulstealer actually works on her because you should almost never die. i still don't get it in serious games but it's certainly an option. your effective range is great, so you can afford to go very light on defenses.
absolutely do not get an evil tome first.
absolutely do not get a tear of the goddess first (and probably ever).
absolutely do not get a rod of ages, ever.
sorry i see way too many pubs getting those items. you need as much ap as possible as quickly as possible to stay ahead of the curve.
4. Any tips?
in lane, you want to land e a lot (qe/eq if possible, even q -> auto -> e if you're close enough) and if possible get out a quick autoattack for the bonus damage. but be aware that your mana costs are pretty hefty, so spamming may not get you too far against lane opponents with good sustain. if you're duolaning, you want to be with someone who can take advantage of your landing your skills to do a lot of damage. the shield helps you get out of bad situations, but never -count- on it; the amount shielded isn't huge and it doesn't grant any resists or anything. also try not to use abilities pointlessly, since your cooldowns are really long and a good opponent will take the opportunity to punish you or zone you for a while. oh yeah and a high-level e + one autoattack farms caster minions, but of course you usually don't want to push like this. e is also nice for blowing up wraiths past the earlygame.
once you have your r, you have fairly good burst in the form of qer/eqr (pop e after the r since there's a short delay before you can pop it anyway). note that the q bounce is only 1 second long, so the secondary hit is generally not enough to land this. r is also useful for stealing buffs/dragon/baron (though you're probably not going to beat out a smite) and for clearing lanes before recalling. be aware of when you can guarantee an r hit even without landing cc - close to a wall, around a corner, etc. also know when it's possible to get close enough to a far-off fight to help out with an r. this is mostly about just being familiar with the range, but yeah. it's kind of lame but the range indicator cuts out in the middle, and you only see where the laser starts and ends.
in a teamfight, your role is to stay behind everyone, shield the opponents' focus target (of course it's ideal to just shield everyone but a good team will be going for one person, and you want to make sure you get both hits of w on that person), and use everything else as you see fit. that is to say, you have a lot of options to control your fight, and whom you should snare/slow depends greatly on the situation. but in general you want to throw out q and e and then r as many people as possible/the high-priority targets. unless you're sure you're safe, absolutely do not go in to try and get passive procs: they do relatively little damage, and it's suicidal. you're at your best when the other team lines up for you, so all else being equal you prefer to fight in narrow places.