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So everyone here is a league member, and that means you'll need to be able to form and use a competitive team, since you're limited to 2 wild card pokemon. This doesn't mean you have to choose the pokemon suggested in this thread, but it is reccomended that you at least read through this guide to understand what goes in to making a competitive team so that you can make your own informed decision.

Firstly, you need to decide what sort of team you want to form. Will it be a weather team so that your fire type advantage is maximized by a drought ability pokemon? Or will it be an entry hazard setup team, where you use your bug/rock/ground/poison type pokemon to lay down spikes, toxic spikes, stealth rocks and other annoyer moves like hypnosis and leech seed. There are many different strategies you can employ for your team, but you need to find one that fits your type advantage.

The most common team setups are listed below.
1. A weather team. This team uses the weather abilities (drizzle, drought, sand stream, or snow warning) or the weather moves (rain dance, sunny day, sandstorm, or hail) in combination with specific rock held items(damp rock, heat rock, smooth rock, icy rock) to extend the duration of the weather moves. Weather teams aren't just for type effectiveness, you can use a weather team to prevent your team from taking full damage from its weakness type. For example, if you had a drought ninetales in your party to summon sunny day as soon as the battle started, it would allow you to instantly use solarbeam without charging up as well as reduce water damage by 50%. This would benefit a ground team, a rock team, and a grass/bug team, and *also* a fire team. All weather conditions are like this, none are exclusively beneficial to a single type. In combination with boosting abilities (swift swim, dry skin, hydration, rain dish, chlorophyll, flower gift, leaf guard, solar power, sand veil, sand force, sand rush, ice body, snow cloak) a weather team can devastate opponents, even when they have type advantage.
2. An entry hazard team. This team sets up entry hazards when it first enters the field, like stealth rock, spikes, and toxic spikes. Once set up, these moves will damage your opponents by taking a percentage of their health, damaging them based on move type effectiveness in the case of stealth rock, and potentially poisoning them as well. This limits them from using strategies like the Regenerator ability with U-Turn, using moves like wish, heal bell and baton pass.
3. A trick room team. This team relies on their own pokemon's low speed by using the move trick room to reverse the order of attacks. This works great for heavy hitting sweepers that have a very low speed stat.
4. A defensive set up team. This team uses the moves reflect, and light screen while holding light clay to lower physical and special damage by half. It may also use moves like substitute, protect and detect to lower damage taken further. This works well for teams with many type weaknesses, or 4x weaknesses.
5. A status impairing/ailing/annoying team. This team will use moves like Leech seed, toxic, will o wisp, thunder wave, curse, fire spin, whirlpool, and wrap to continually damage opponents. This is the ideal strategy for a team with high defenses and hp and low attack.

There are many other strategies, but these are the most well tested and effective of them.

The third thing you should consider while building a competitive team is your pokemon's movesets. You can't have a team that has only offensive attacks(all sweepers), if someone confronts you with a team that uses moves like mirror coat and counter (or several other strategies, endure and flail) your team will be gone in seconds.

Your pokemon need to have at least one attack/sp atk, but probably no more than 3 unless they are sweepers(and we've already established that having a team of all sweepers is a bad idea). So what should that last one or two moves be? Here are some ideas to get you thinking.

1. A recovery move. This will save your bacon if your pokemon is a high overall statted sweeper. When you take one or two hits with your high defense and get down to half health, you can use the recovery move to outlast your opponent(even though you'll take another hit in the meantime.) Popular recovery moves include moonlight, recover, rest(especially in combination with sleep talk or snore), and roost.
2. A stat boosting move. Sword dance, amnesia, quiver dance, teeter dance and curse are the most popular. This will give your pokemon enough extra killing power to eliminate more than one of their pokemon, which will put you one pokemon ahead in the battle.
3. A status ailment/impairment. Confuse them. Flatter them. Paralyze, burn or badly poison them. Putting them to sleep will give you 1-3 turns of an advantage, although you will only be able to put one pokemon to sleep at a time(smogon rules). It may not be immediately apparent how useful these moves are, but they will make the difference between whether or not their pokemon outlives yours.
4. A weather inducing move/trick room/entry hazard. Perfect for setting up a weather or trick room team.

Now that you've got your team built, with the right movesets and abilities, how do you use it?

Really, it depends on what you're up against. If you're facing someone with type effectiveness(like you probably will since each trainer is forced to use at least 4 of a single type), you should either start with one of your wild cards, or use a battling strategy like setting up entry hazards, trick room, or defensive barriers first.

If you're facing a sweeper, use a faster sweeper(or one who has type advantage), or a staller like Blissey or Breloom to eliminate the threat with only minimal damage.

If they use a stat boosting move like sword dance, quiver dance etc, send out someone who can either kill them quickly or punch through their weakness(whether its sp def or defense), or use mist/snatch/haze.

If they're setting up entry hazards on you, use rapid spin/defog, or the magic bounce ability.

If they're using a trick room team to sweep, send out a wall/tank who can outlast the duration of the trick room(5 turns), or your slowest pokemon and hope to move first.

If they're using weather conditions, send out someone who will take low damage or benefit from them, or use your own weather conditions.

There are so many pokemon moves and abilities that I can't possibly list them all here. However, if you see them send out a pokemon that you don't know how to counter, I reccomend looking up that pokemon's abilities, stats and movesets, then choosing someone who has at least one move that is type effective against it.