Bring water. At least two bottles for on the trail itself, and have some ready in your car for refills. Helmets might look dumb, but trying to scrape your brain off of a rock or tree doesn't seem very cool either. I have a few scrapes on the top of my lid where I misjudged the height of low hanging branches and probably missed a nice scalping.
I like to have a small backpack with some food bars and minor tools for field repairs and adjustments. As a beginner, you aren't likely to notice many tuning issues while riding, so tools can be optional. You may want to lower your seat a bit to give you a bit more room to move around on the bike. Don't forget to stretch a bit before hitting the trail, cramps like to sneak up and visit when they aren't expected.
Downshift before climbing a hill so you don't lose momentum and stall if your chain misses and derails. Riding down is fun, watch out for rocks, roots, logs and holes, though. For steep downs try to shift your weight a little more rearward. Don't mash the brakes - a rolling tire has more control than a skidding tire.
