Am I telling you to get the Zeppelin as your first pet? You bet I am. But if you have something else, I'm sure it'll work out fine. Just make sure that it's easy to play -- focus on the harder things later on.
The next step in getting started is the longest task you'll have in pet battles, getting your first pet to level 25. Or at least it seems like the longest task. You'll need to battle every trainer you can (most of the time I found you can just power through them with your one pet, although you'll run into specific instances where you want to switch to other more appropriate pets along the way -- more information on strong and weak pets is in a great guide at Warcraft Pets). Use the map to find zones with pets at or slightly below your main pet's level.
You'll hit a wall with the trainers around Northrend, and that's ok. Just stop there and grind out any remaining levels on your pet (if you have any, I didn't). As your leveling be sure to capture every unique pet you come across. If you don't have it, capture it. You're not just collecting for the sake of collecting either, you'll need an absolutely army of pets later on.
Nonetheless, getting that first pet to 25 is key. Why? Because when you've reached 25 on one pet, you can use it to capture other level 20-ish pets, and then start forming your teams.
Your first battalion
To me a pet battle battalion is a group of 10 rare pets encompassing all of the 10 different pet classes. This is really important in order to defeat all the trainers throughout the entire game. When you're fighting against epic and legendary pets, you'll rarely stand a chance without having a pet that's perfectly matched -- and you'll stand no chance if you're on the short end of the stick (ie: if you match your beast pet up against a mechanical pet).
The biggest thing to consider when making your first battalion is to have them all be pure pets as much as possible. By this I mean make sure your beast pets can do three attacks of beast damage, your elemental pets can do three attacks of elemental damage, etc... This might sound odd -- like it should be something that is done automatically, but in reality that's not the case. There's a lot of pets out there that, for instance, only have one human attack ability when they're humanoids to begin with.
And I'm not saying that those pets are not useful (they are super useful later on), but to begin with make sure that you're starting with a solid foundation. Don't do what I did and get a magic pet that looks cool but has no offensive magic abilities. You'll pay dearly for making such poor choices.
To actually pick your battalion you'll want to meander through your pet journal and see what you have. Plan out your entire battalion and set each pet as a favorite so it lives at the top of your list. Then head out to Pandaria and find some level 20-ish pet to battle with your low level pet going first. When the battle starts do one round of damage with it, then immediately switch to your other more powerful pets. You'll find that your low level pets will become maxed in about 30 to 60 minutes.
It's really not hard at all to amass your first battalion this way. Put on some TV, grab a cup of coffee, and just start going. You'll be finished in a couple days (or if you're like me, around 4am the next morning).
Kill them all
The next thing you'll want to do is hit up all the other pet battle trainers you weren't able to defeat. Remember when I said you'll get stuck around Northrend? That's where you should pick up at and start clearing out the rest of the trainers. It'll be nearly trivial with your perfect base battalion you made. Look up the trainers on Wowhead before head out if you want to see what pets you should enter the battle with, or just enter the battle once and forfeit immediately so you can see for yourself (you don't take a HP hit if you do this with a trainer).
After you've defeated all the trainers through Pandaria, you'll hit another wall where you'll need additional pets and specialize your teams a bit. You'll need to start learning about combos, buffs and debuffs, and get into the breeds (a variable determining if your pet has high speed, health, and/or strength).
Immediately following the normal battles are the Pandaren Spirit Tamers -- and they're not pushovers. You'll need another specific pet or two in order to defeat them (we'll cover this next week). They also require some luck, although with the right breed you'll be able to beat them on your first try.
Then comes the Beasts of Fable, which you're going to need basically 15 pets maxed at level 25. Now this might seem like a lot when you've only got one pet maxed, but in reality the leveling process goes very quickly as I've said before. So don't be intimidated.
And finally comes the Celestial Tournament, where you're going to need an army of maxed level pets, in my opinion between 30 and 40. That one is intimidating no matter what vantage point you're looking at it from. But it's meant to be a challenge -- and one that takes you from a simple game of battling around Azeroth and Outland to defeating raid-boss like encounters.
Stay tuned next week when we'll cover the Pandaren Spirit Tamers, along with my specific pet list.