I would bring a 20-sided die (or one of the specially-made life counters that have the numbers conveniently arranged in a spiral, if you have one from a fat pack or something) to track your life, or paper and pen. Also, some way of determining who goes first; try not to use one of the life counters for this, since they're not made to roll evenly and the arrangement of numbers makes it easy to cheat (and people are suspicious, so it's better etiquette just to avoid the whole idea).
If you're going to a draft, bring a few 6-sided dice as well, in case you need to keep track of counters on cards. You never know when you'll pull a planeswalker or some +1/+1 counter spewing card, and the dice are typically easier if you've got more than 1 counter on a thing. If you're playing Constructed, you can make this decision based on what's in your deck. Some sort of Boros aggro deck likely wouldn't want to bother, for instance, but a Simic/Golgari one would be rude not to.
If you want to sleeve, bring at least 40 of them, and practice doing it quickly so you can get it done during deck assembly. I do, but only because I can't shuffle efficiently, and it's important to be able to go fast when randomizing your deck, as a matter of courtesy. If you've got a good group of players, they'll be happy to answer your questions about more specific etiquette and the mechanics of the draft tournament. Just mention it's your first time and hopefully they won't be douchebags about it. If you don't have good players, you'll have a lousy night, but you might not want to go back to that store anyway unless the cardboard crack has really got its claws in deep (drafts are often cheaper than straight-out buying the packs, you see).
Technically, you're not supposed to look at your card pool except between packs when drafting, by my understanding. My place doesn't care - I'd suggest asking, or if you feel embarrassed enough, just watching to see if anyone else is as a cue.