How dangerous is it to fall 3 meters when lead climbing?
This depends a lot on the fall factor. Counterintuitively, the fall factor is higher, indicating a more dangerous fall, when you are near the beginning of a pitch. This is because there's less rope out, so there's less stretchiness.
As Steed's comment points out, you're going to fall more than 6 m in this situation, not 3 m. After you get your first clip in, you may have a false sense of security; by the time you're reaching for the second clip (which is 6 m up in the situation you've described), you have enough rope out so that if you miss the clip and fall, you're going to hit the deck.
Different falls can have different run-outs. A fall from an overhang is actually the safest, since you can't hit anything. Depending on the route, you could swing like a pendulum, or slide down a slab and get cheese-grater injuries.
What protection equipment should be used.
A helmet. If you're trad climbing, that's a whole different thing -- we'd be talking about a trad rack.
What training exercises should be completed beforehand?
Start by learning to give a lead belay, and practice doing that enough times so that you understand the whole process well. Learn by watching your climber while belaying. Discuss things verbally with your climber. Help your climber catch mistakes.
Learn not to back-clip, z-clip, put your thumb through the biner, or back-step the rope. Spend some time at home practicing clipping efficiently in a variety of positions with a quickdraw hanging on a doorknob.
If you do fall, absorb the impact against the wall with your legs, and don't grab the rope.
Learn the steps involved when you get to the top of a sport climb. This is actually pretty complicated.
There are some advantages to learning to lead in a gym. For example, the routes tend to be constructed so that the run-outs are very safe, there is no danger from rock-fall, and you don't have to worry about the quality of your anchors.