Out of my (Pokemon) League?

the above mentioned websites are good resources. serebeii.net can be a lot of help too. June 4th is kind of close. Unless you plan on playing a lot, it will be difficult to assemble a half decent team. Heres some things you will need to look into:

EVs (effort values) - In a nutshell, when you kill pokemon, you get an EV for a particular pre-assigned stat to the pokemon you killed. By specializing which EVs you get, you will be putting certain stats on steroids.

IVs (Individual values)- Not all Pokemon were created equally.

Nature- pokemon natures hinder and boost particular stats so you need to make sure you have the right one

General Strategy- Spikes, Baton Pass, Haze, etc.

When picking your Pokemon, go to google and type in [Pokemon of your choice] Pokemon of the Week (ie Garchomp Pokemon of the week). serebeii has some very good articles on each Pokemon.

Watching youtube videos of people's teams is also not a bad idea.

In general, it'll be pretty difficult to get yourself ready in time and not make a fool of yourself, but its doable. And its a lot of fun so go for it :D

Before June 4th? Possibly, but not likely.

There's a ton you have to learn when it comes to competitive battling. More than you think. Not just the IV/Nature/EV training factor. You have to learn about different roles, different sets, counters, strategies, tiers, how your team will work together, all sorts of things.

You could look into Smogon, or something. They're all about competitive battling, and I'm sure they'll help you. It takes time, though. And a lot of practice.

Also, don't be cliche. Try to make your team unique, but work well.

And yes, that means you don't need to have Conkeldurr, Reuniclus, Blissey, Garchomp, Latios, and Excadrill all on the same team.

For competitive battling you can't go wrong with Smogon. The 5th Gen hasn't been completely tested but it gives you an idea of the best teams avalible.