Play how you want, and have fun. Pokemon, like any video game, isn't worth playing if you don't have any fun with it. If EV training, IV breeding, shiny hunting, and all the rest of the purely optional and unimportant stuff is enjoyable for you, then go for it. If it isn't, don't get hung up over it.
Pokemon is a very simple series when compared to other JRPGs. Once you've learned the basics, you can play however you want. So go for it. Discover your own play style and enjoy yourself. Don't worry about your levels vs. your opponents, don't worry about what your Pokemon team is like, hell, don't even worry about type matchups if you don't want to. You'll learn through experience and discover what best suits you as you go.
It took me until the fourth generation to stop worrying about how everyone else was playing. You'll get all sorts of recommendations about how to make the game easier for you, and it's perfectly good advice, but it's still all totally unnecessary. The best way to learn is through your own experience. Some people like to play with a team of their favourites, some like a balanced team. Some people grind a lot between Gyms, and others rush through. Some people go for the best possible Pokemon by screwing about with hidden values and natures, whilst others never bother with it. Who cares? There is no right or wrong way to play Pokemon.
So, learn how it works and enjoy it.