To trade with someone else that’s not in the same room, you just need to exchange friend codes (Pal Pad) and go to the Wi-Fi room (middle one in the Pokecenter).
The GTS is a clusterfuck of the world’s morons. Stay far, far away from there unless you’re doing Magnemite trading.
As for Gen VI, I’m meh on it. I’ll keep an open mind, but to me, it’s not worth getting a 3DS for it yet. The map still looks tile based, there’s no lead Poke following you, the legendaries look bad (oversized antlers and a sweater wearing bird, really?), and the starters seem bland. I’ll keep watching for more details, but it hasn’t impressed me so far.