Lots of great advice here. One of the things I enjoyed a lot over the years was seeing parents playing with their kids (usually dads, but not always). As we all know, teenagers and their parents often have trouble keeping the lines of communication open. One reason why is that there is less and less common ground based on shared interests. Paintball is great in helping in that role as it provides an easy way to spend a memorable day together.
Another point that makes paintball great for family outings is that it doesn't require a special skill set to play and have fun. (DISCLAIMER: I'm talking about at the walk-on, rec / woods- ball level.) Even bowling requires more sport-specific skills of the beginner to not feel like an idiot, and any walk-on rental player stands a fairly good chance of shooting someone his first day out.
In addition to all the other good advice in this thread, I'd like to add that it's a good idea to check the paintballs before you buy. If they are visibly disfigured (out of round, dimpled, wet with broken paint, any of which will make it essentially impossible for the balls to fly straight.), I'd recommend buying a different box, or if necessary, getting the next grade up. Nothing spoils a day of paintball faster than bad paint.
Now that MCB is connected with Paintball News, maybe someone could compile all the advice in this thread into an article and get it to them for publication? It seems that a free newspaper that a would-be player can grab at his local shop and hand to a parent has at least as good a chance of making a difference as trying to get said parent to log onto here.
One final note about the gun safety training: One of the fundamentals of gun safety is to always treat a gun as if it were loaded. There was a case here in Japan a few years ago on one of the US Military rec-ball fields where two 12-year-olds were fooling with their markers in the staging area. They hadn't been given any paint yet, so saw no need for a barrel sock.
Figuring a blast of CO2 by itself was harmless, one of the kids shot his friend in the face. At close range (point blank), the pressure was enough to actually force the eyeball from its socket. The kid was rushed to the hospital, but doctors were unfortunately unable to save it. 12 years old.