Get the Right Gear
There's nothing worse than getting 3/4 the way up a climb and running out of gear. Always take more than what you'll need. Especially if you don't know whether most of your clips will be on the right or left side. If this is traditional lead, then I recommend planning and organizing your rack very carefully. Perhaps even investigating others to find out the ideal rack for the route. For most sport routes, some climbers are content to use two draws with gates opposed. I often do this myself. However, traditional anchors are far more complex and should be planned out carefully. In fact, if your first lead is on trad, I suggest you get intensive training on setting up anchors if no bolts are available.
Understand Backclipping Before You Leave the Ground
I don't know how many times I have had to explain backclipping to people who are already beyond their first bolt. It is a realistic threat that with bent-gate biners, your rope could slip out of the gate.
Have a Capable Belayer
Even though you think you're psyched and ready to go, how about the bumpkin belaying you? Are they quick enough to save your life if you fall? Can they give you the advice and moral support you'll need when your legs start quivering like jello?
Focus on Climbing, Not Falling
Falling is always a threat, but if the route is well protected, and your belayer is competent, your fall should be safe. If you're not convinced, try it. Just let go. Take a deep breath, warn your belayer, "Falling!", and push out. "AAaaagh!" Thud. Whew! You breathe, and then you start to smile. "Wow. That wasn't so bad after all." Falling on natural pro may take a little more convincing, but if you don't trust falling on it, then you shouldn't have moved past it.
Be Prepared for Failure
And I don't mean emotional failure. I mean, what are you going to do if you can't finish the route? Will your partner be able to finish the route? Can someone nearby save your gear? Or will you need to leave a bail biner? Sadly enough, this should always be taken into consideration.