Ranok wrote:My strategy would be to stone your Panther Cub
That was my answer too, of the OP's existing pets.
http://eu.battle.net/wow/en/forum/topic/17611961961#2
I suspect we will be seeing more of the "what should I use my first stone on" questions in the opening months of Legion.
I gave a longer and more general answer elsewhere. I'll paste an updated version here for future reference.
For a complete beginner, with no 25s, these are the pets I would make a priority to buy or farm, and level. There are many other great choices, but these
a) can all be traded, so you don't have to find and capture
b) are well known and used in common strats and guides
1. All-rounder: [pet]Anubisath Idol[/pet]
My personal choice, if I was starting again, would be Anubisath Idol. It's not that it's unreasonably overpowered; it's that it's a solid, tanky, all-rounder, and especially because it can protect a lowbie pet you're levelling with its Sandstorm. It's not best at anything, but it is good at everything, and that's invaluable to a beginner with just a few pets.
It can also face any tamer without fear, and it's especially good against the Pandaria tamers. I think it can solo any of Erris's teams. It comes in Blue as standard. Its downsides are that the default moveset isn't great against Beasts, and, let's face it, it's a bit boring to play (but that makes it easy for a beginner battler.)
Mostly, I'd go for this first because it's hard to live without at top level PvE play, so it needs to be one of your first pets anyway.
You can buy a level 1 at the AH for a couple of K, or you can solo AQ40 for about a 10% drop chance each week.
2. Capturing: [pet]Terrible Turnip[/pet]
If you have a[pet] Molten Corgi[/pet], that will serve the same purpose.
Terrible Turnip is cheap and plentiful at the AH, and comes as Blue quality. It is not anything like as good an all-rounder as the Idol, but the Turnip and the Corgi are the two pets that have an attack that cannot kill an opponent, but just drop its health to 1. This means that any taming team for capturing pets in the wild benefits hugely from having one of these two.
If you propose to spend a lot of time in the near future capturing and taming a hundred or two wild pets, the Turnip is worth considering.
3. Farming pet levels: Any Cat, or beast with Devour, like [pet]Zandalari Anklerender[/pet]
The great thing about the [ability]Devour[/ability] ability is that it restores health to your pet when you kill, so it lets you keep on grinding wild battles without stopping to visit the Stable Master. Just make sure never to kill except with Devour, and your beast will keep on tickin'.
Cats pretty much all have it.
You can buy Green-quality cats cheaply from vendors, but you don't want to boost a green until you have enough pet charms or stones to make it a Blue. The most powerful of the cats is the [pet]Cornish Rex Cat[/pet], but if you have the gold, the [pet]Feline Familiar[/pet] is especially versatile, with a strong attack against Flyers as well.
You can buy a Blue Zandalari Anklerender very cheaply (less than 100G?) on the AH, or farm Isle of Giants for some drops yourself. My preference is for a P/B breed, but a P/P is also excellent.
These Beasts with Devour are amazing for farming the Critters just west of Halfhill.
4. Farming pet levels: [pet]Teroclaw Hatchling[/pet]
The Teroclaw can be picked up on the ground in Talador, or from the Auction House very very cheaply. It's one of the most overpowered PvP pets in the current game when used with Alpha Strike / Dodge / Elemental Ward.
With Alpha Strike / Dodge / Ravage it is a great farmer of Aquatics.
With Claw / Dodge / Ravage it is a great farmer of Critters.
The idea is to use [ability]Ravage[/ability] as you would use Devour - never kill with anything else, and Ravage will keep your health topped up endlessly. Use Dodge to avoid any two-round nukes your opponent throws at you.