First of all ... good luck! Experience suggests that you'll get the bug and be doing the whole thing yourself soon enough!
As hinted above, the most advantage to be gained is in the aero position on the bike. Assuming you have a road bike (and if you don't, borrow one in the
correct size) the biggest bang for your buck is probably tri-bars. When riding on the hoods on a road bike, your body acts like sail. When you stretch out on tri bars, you reduce the all important frontal area. Also, remove all unnecessary paraphenalia from the bike - I am amazed at people I see racing triathlons with a D-Lock and lights
Next up in terms of time savings per pound spent (if memory serves - and I apologise, I cannot find the studies I am thinking of but shall keep looking) is an aero helmet. This came as a surprise to me, but if you can borrow one, it's apparently worth it.
Aero wheels make a difference, too. As mentioned above you have to match the wheels to the race conditions to get the most advantage.
The biggest difference I noticed when going from an ill-fitting road bike with drops to a properly-sized bike with aero bars was that the bike-run transition was a LOT easier. Those elusive articles suggested that a triathlon bike can save around 2 minutes on a 40 minute 10km run by placing more emphasis on your cycling muscles, leaving your legs fresher for the run. I was amazed at the effects. Clearly, this won't affect you on the relay, but one to think about if / when you get the bug.
Final advice is to know the guys you're racing with to make the baton (usually a rubber band, or timing chip) handover easier! Agree a place to stand in the transition area, and know the local rules about when / where you can be on your bike, where you can't etc. around the transition area
Off to search a bit more for those articles