How I become a PC Gamer?

I want to know how to become a PC Gamer, because I want to be able to play the newest strategy games, online action games, some pc-exclusive, and if I'm able to get a good PC, every type of game.

I want a laptop so I can take it to my living room, bed, kitchen, on holidays, to other places, so I don't want a desktop or a super heavy computer. I'm not sure of my budget, if I convince everyone in family just to give money, my parents to give me some too, if I use what I've been saving, I may get myself a 1050€ laptop PC (probably a MSI GE60 2PE Apache Pro).

I want a PC with a full hd matte screen, atleast a GT750M, an Intel Core i7, a dvd port, etc, so what should I get?

If I don't spend all my money (I guess I won't have more than 1100€ by mid-june), what periphals I should buy, if it's worth a gaming mouse and headset, what games I should have (the only one I truly want is Civ V complete edition)

So please help me.