You can't change IVs, that's going to be a post-game thing with bottle caps like the main games*. But IVs aren't really super important, just don't settle for 0 in your relevant stats (I personally try to get above 15 in relevant stats personally).
The fastest way to EV train most Pokemon is to grab the power items from the department store's 4th floor (So once you get two stickers, which is doable before Shelly), and then go fight the static Woobat encounters down in the underground. Set the game to Fast Forward (default is the left alt key), and turn off animations. Which means 63 Pokemon for all non-speed stats and 51 for speed. Unfortunately there's not really a faster option.
*At least I think that's been said, but now I can't find it, so you might just not be able to change IVs at all. I know that in the past Ame's said she doesn't like the idea. But like I said, IVs aren't really super important since the effect on stats of say a 25 vs a 31 is a small 6 points.