EV's/IV's/Nature are definitely significant, at this point in the game, but are not some magic formula that will make any team capable of winning any battle in game. What a proper spread will do, is it will ensure your team performs how you expect them to and will increase your consistency. Most of the time in Reborn, you can compensate by using boosting items and potions if your strategy is sound.
That is not to say that you shouldn't do it. Like Rayu said, EV training will help a lot if you aren't experienced in competitive play. If you do want to try to EV train, my recommendation is to use the power weight items from the department store and farm the woobats and noibats in the shadows under the railnet since they always give 1 speed EV and you can guarantee their spawns.
Fishing is also a pretty good option, but i don't know all the fishing tables so i'm afraid I can't tell you which spots are best.
As for recommendations for the fight