P3 = Phantom 3. There are currently 3 different P3's. P3S = Standard, P3A = Advanced and P3P = Pro.
Lots of people suggest getting a cheap one to learn on. I had a Syma x5c I think it was called. I don't know what I really learnt to be honest. I learnt they are junk but very durable. The batteries last about 5 minutes and the flying is very hard. You'll likely crash into every thing imaginable. The good thing is they are pretty much indestructible. I hit my house, my shed, numerous trees, my ceiling, my dog...pretty much anything and everything. Whatever you do have fun with the toy one but the P3 or P4 you get will fly 100x better and be 100x easier to control. But you do learn the basics flying the cheap ones so its not all a waste.