Firstly you need to figure out which format you want to battle in. Though unofficial, I believe smogon is the most popular format. Smogon is a singles 6v6 format separated in to tiers due to the usage of pokemon. They are separated in to the tiers Ubers (The OU banlist), OU (OverUsed), UU (UnderUsed), RU (RarelyUsed), NU (NeverUsed), PU (The bottom of the barrel). In OU for example, you can use anything from the tiers below (UU, RU etc...) but can't use things in Ubers. There are also certain rules such as species clause (One of each type of Pokemon per team), Sleep clause (You can only set one Pokemon on the opponent's team to sleep at a time excluding rest) etc. The clauses in effect change between each tier.
Unfortunately if you wanted to use Mega Mawile, you would need to play in the Ubers format as Mawilite was banned from OU. In this format, every Pokemon except Mega Rayquaza (It was far to OP) is allowed and there are far fewer rules. Mawile is a bit underpowered in this format and so is rarely seen.
If you're comfortable with doubles battles, VGC is probably for you. VGC is the official format for competitive battling. It is a see 6, bring 4 type format (As in, during team preview you select 4 Pokemon you want to bring from your team of 6). As of VGC15, these are the rules:
http://nuggetbridge.com/news/standard-ru...n-updated/
I believe there is a distinction between VGC15 and Battlespot Doubles, where the pentagon rule isn't enforced.
In this format, Mega Mawile is allowed and is a strong pokemon, considering its pre-evolution ability of intimidate being amazing in doubles, having the highest base attack in the format when taking into account its Huge Power ability and pretty amazing typing. If you intend to use Mawile, you should look in to running some form of speed control in either Trick Room or Tailwind. I won't go too in detail about team building as I'd be here for a long time, but take a look at this if you're interested:
http://pokemonforever.com/Thread-VGC-VGC...015-Revamp
Sorry for the huge response, it's just competitive battling involves different rulesets depending on the format you choose.
A good place to start before breeding anything is Pokemon Showdown, a battle simulator where you can make teams easily.
For information on what each Pokemon is likely to carry, look on that smogondex that Logoff linked, searching for particular Pokemon. Make sure you look at the correct format that you wish to play in.
If you don't understand anything I have said or need any questions answered, post here or feel free to PM me.
