Like most times when I start a new game, I'll train my Pokémon to reach a certain number of levels higher than the Gyms and Elite while gradually grinding in between so as to not fall too far below the standard level curve. That being said, I pray these games come with a well balanced level curve that makes grinding not too easy, but at the same time not too hard or tedious. I've always felt like that's one of the main drawbacks with Gen II and again in HG/SS. I hope X and Y don't follow that pattern.
I find EV training too difficult at the start, because you're limited to only a certain number of Pokémon to train with. Plus, you can't always control who you run into and who you'll battle next as the storyline goes along. While I'll probably soft reset and search for Pokémon with beneficial natures, I'll save any EV training for post-game. At least that way I have more control over what I battle and it'll give me something extra after the main story is done too.