I haven't actually done any of the new WoD trainers so I can't offer any suggestions there but I will say that the more difficult part of what you are asking for might actually be defining "Common", "Easy to get" and "Cheap" as opposed to coming up with the actual teams. After all, nothing is easier to get than a pet you already have. Cheap can also be vastly different depending on what the person has to spend and what their servers economy is like.
I'm sure that there are some wild pets where it would be easy to get a consensus that they aren't easy to get, such as the Unborn Val'kyr, but there are also a number of pets where it won't be as easy to say. For example is a Flayer hatchling easy to get or not? On the one hand I'd say no as there are a decent amount of spawn points to get you one. On the other hand it's a pet where breed can be very important as you probably want to be faster than your opponent. Since it comes in all possible breeds getting a rare s/s in the wild is not particularly easy. If you have a stone to use getting a S/S breed of any rarity and then upgrading it shouldn't be bad but that isn't necessarily the easiest thing in the world for someone new to pet battling. Granted you can now buy an upgrade stone after only a couple days even if you can only beat one or two tamers initially.
This was the kind of thing I dealt with when writing my CT guide below. For my guide I ended up using a Fel Flame which I felt was kinda a middle rarity wild pet. It certainly wasn't an Unborn Val'kyr but it also wasn't exactly common either and was pretty spread out in the zone. I didn't really want to use it but in the end I couldn't find any replacement pet with good dragonkin attacks that wasn't a dragonkin that I felt was any easier to get. An MPD is a great replacement but it has to be bought and probably stoned which is why I didn't want to use it.https://docs.google.com/document/d/1WRF ... sp=sharing