Just curious...

1.) Are chip timing straps provided or does it depend on the race? 
Yes, at every race I've been to, the straps are provided.
2.) Any recommendations for a good pair of tri shorts?
Male, Female, size, etc would probably help in determining this one.  I wear either Pearl Izumis or 2XU Comp Shorts.
3.) Any pre-race jitters advice? Just thinking about it is starting to give me butterflies!
Remember in Finding Nemo where Dory said "just keep swimming, just keep swimming" and she wasn't nervous or anything?  Channel Dory for your first race.  Just keep Swimming, Just keep riding, Just keep running.

I've found that veteran triathletes are very willing to help new ones setting-up transition and will talk to them about anything if they just ask for help and ask questions.  A lot more than cyclists, Wrestlers, etc where you have to be of their class to get help.  I don't know why that is, but I've had good experiences in pre-race and have witnessed a lot of good acts prior to a race where a new triathlete is helped by a veteran.

Just breathe, do what you can, hydrate before during and after, and finish. 

1.  As has been said, they'll provide the strap.  Sometimes, though, it is one of those plastic snap-closure wristbands (like you'd get at a hospital) rather than the velcro-and-neoprene kind.  If you don't like that kind of band (they can sort of dangle if there isn't a hole at just the right size for your ankle), you could use your own, but I never have.

2.  I'm a big fan of Zoot shorts, mostly because I really like the small mesh side pockets.  But also because they're well-constructed.

3.  Relax.  Visualize your race (esp. your transitions).  And really, really, breathe and center...and relax some more...before the swim.  Don't know if your tri is a pool swim or open water, but it's almost impossible not to get really jacked up by your first OWS wave start and that can lead to hyperventilating and--for some people--even a little panic.  It's almost impossible to replicate the conditions of the swim start in training, so just really talk to yourself before the start to plant the seeds for remembering to settle down once you've gotten started...remind yourself to let go of the inevitable adrenaline rush of the start once you are underway.

Good luck.