I’ve dived into the deep-end for breeds and pretty much decided I want the highest speed breed first, the highest power breed second, and if the highest speed & power breed are the same breed, I take the highest health. I keep no more than 2 of any pet (I ran into issues with the pet cap when trying to do 3). The one exception I make is that if there is an H/H breed, I’ll take it as one of my two pets unless there’s also an S/S and a P/P (in which case I take those two).
Beyond that, there are a few breeds that perform well that I would not pick up following those rules. In those rare cases, I will make exceptions to my rules and pick one of those breeds instead. These pets are usually found while browsing Xu-Fu’s Pet Battle Strategies website. They’ll either appear on the PvP Pet Tier list or in specific strategies for harder Pet Battle encounters/dungeons (for instance, Family Exorcist achievement in Shadowlands).
EDIT: There are also different pets that have the exact same abilities, here’s a list of those incase you wanted to make sure you covered all breeds across the pets:
Bandicoon:
Auburn Ringtail, Bandicoon, Bandicoon Kit, Masked Tanuki, Masked Tanuki Pup, Shy Bandicoon
Bat:
Bat, Echo Batling, Hog-Nosed Bat, Tirisfal Batling
Beetle/Roach:
Beetle, Cockroach, Creepy Crawly, Crystal Beetle, Death’s Head Cockroach, Deepholm Cockroach, Dung Beetle, Fire-Proof Roach, Gold Beetle, Irradiated Roach, Locust, Resilient Roach, Roach, Sand Scarab, Savory Beetle, Scarab Hatchling, Stinkbug, Tainted Cockroach, Tol’vir Scarab, Twilight Beetle, Undercity Cockroach
Bile Larva:
Antoran Bile Larva, Bile Larva, Fossorial Bile Larva
Buzzard/Parrot:
Blue Mini Jouster, Cockatiel, Dragonbone Hatchling, Fledgling Buzzard, Gold Mini Jouster, Green Wing Macaw, Hyacinth Macaw, Parrot, Polly, Senegal
Cat:
Black Tabby Cat, Bombay Cat, Calico Cat, Cat, Cheetah Cub, Cornish Rex Cat, Darkmoon Cub, Nightsaber Cub, Orange Tabby Cat, Panther Cub, Sand Kitten, Savage Cub, Siamese Cat, Silver Tabby Cat, Snow Cub, White Kitten, Winterspring Cub
Chicken:
Ancona Chicken, Chicken, Szechuan Chicken, Westfall Chicken
Crab:
Emperor Crab, Shore Crab, Shore Crawler, Sparkleshell Sandcrawler, Spirebound Crab, Strand Crab, Strand Crawler
Dragonhawk:
Blue Dragonhawk Hatchling, Golden Dragonhawk Hatchling, Red Dragonhawk Hatchling, Silver Dragonhawk Hatchling
Eaglet:
Fledgling Kingfeather, Fledgling Oliveback, Golden Eaglet, Skyhorn Nestling
Firefly:
Effervescent Glowfly, Firefly, Mei Li Sparkler, Shrine Fly
Fox:
Alpine Foxling, Alpine Foxling Kit, Arctic Fox Kit, Black-Footed Fox Kit, Fjord Worg Pup, Fox Kit, Mist Fox Kit, Worg Pup
Frog:
Biletoad, Frog, Garden Frog, Horny Toad, Huge Toad, Jubling, Jungle Darter, Leopard Tree Frog, Mac Frog, Mojo, Small Frog, Spotted Bell Frog, Toad, Tree Frog, Wood Frog, Yellow-Bellied Bullfrog
Glowfly:
Darkmoon Glowfly, Sapphire Firefly, Violet Firefly
Junglebeak:
Axebeak Hatchling, Bloodbeak, Crackers, Fruit Hunter, Junglebeak
Lizard:
Ash Lizard, Diemetradon Hatchling, Horned Lizard, Lizard Hatchling, Plains Monitor, Spiky Lizard, Spiny Lizard, Twilight Iguana
Moth:
Amber Moth, Blue Moth, Crimson Moth, Forest Moth, Fungal Moth, Garden Moth, Gilded Moth, Grey Moth, Luyu Moth, Oasis Moth, Red Moth, Silky Moth, Swamp Moth, Tainted Moth, White Moth, Yellow Moth
Otter:
Golden Civet, Golden Civet Kitten, Kuitan Mongoose, Mongoose, Mongoose Pup, Sifang Otter, Sifang Otter Pup
Owl:
Brilliant Kaliri, Crested Owl, Great Horned Owl, Hawk Owl, Miniwing, Snowy Owl
Rabbit:
Alpine Hare, Arctic Hare, Brown Rabbit, Elfin Rabbit, Grasslands Cottontail, Hare, Mountain Cottontail, Olivetail Hare, Rabbit, Snowshoe Hare, Snowshoe Rabbit, Spring Rabbit, Tolai Hare, Tolai Hare Pup
Rat/Mouse:
Black Rat, Carrion Rat, Fjord Rat, Giant Sewer Rat, Highlands Mouse, Long-tailed Mole, Mouse, Rat, Redridge Rat, Stormwind Rat, Stowaway Rat, Tainted Rat, Undercity Rat, Wharf Rat, Yakrat
River Calf:
Albino River Calf, Flat-Tooth Calf, Mudback Calf, River Calf
Scorpid:
Crunchy Scorpion, Durotar Scorpion, Leopard Scorpion, Scorpid, Scorpling, Stripe-Tailed Scorpid
Scuttler:
Coralback Fiddler, Fen Crab, Frostshell Pincher, Ironclaw Scuttler, Juvenile Scuttleback, Kelp Scuttler, Zangar Crawler
Sea Gull:
Albatross Chick, Imperial Eagle Chick, Rustberg Gull, Sandy Petrel, Sea Gull, Tickbird Hatchling, White Tickbird Hatchling
Shale Spider:
Amethyst Shale Hatchling, Crimson Shale Hatchling, Emerald Shale Hatchling, Tiny Shale Spider, Topaz Shale Hatchling
Skitterer:
Bloodthorn Hatchling, Icespine Hatchling, Mossbite Skitterer, Thicket Skitterer
Slimy:
Slimy Eel, Slimy Fangtooth, Slimy Hermit Crab, Slimy Octopode, Slimy Otter, Slimy Sea Slug
Snail:
Mudshell Conch, Rapana Whelk, Rusty Snail, Scooter the Snail, Shimmershell Snail, Silkbead Snail
Snake:
Adder, Albino Snake, Ash Viper, Black Kingsnake, Brown Snake, Cobra Hatchling, Coral Adder, Coral Snake, Crimson Snake, Emerald Boa, Grove Viper, King Snake, Moccasin, Rat Snake, Rattlesnake, Rock Viper, Sidewinder, Slithering Brownscale, Snake, Temple Snake, Tree Python, Water Snake, Zooey Snake
Spider:
Amethyst Spiderling, Ash Spiderling, Desert Spider, Dusk Spiderling, Feverbite Hatchling, Forest Spiderling, Jumping Spider, Skittering Cavern Crawler, Smolderweb Hatchling, Spider, Twilight Spider, Venomspitter Hatchling, Widow Spiderling
Sporewing:
Cerulean Moth, Crimsonwing Moth, Dusty Sporewing, Skywisp Moth, Vale Flitter
Squirrel:
Alpine Chipmunk, Grizzly Squirrel, Nuts, Red-Tailed Chipmunk, Squirrel
Strider:
Aqua Strider, Dancing Water Skimmer, Eternal Strider, Mirror Strider, Spring Strider
Turtle:
Darkmoon Turtle, Softshell Snapling, Speedy, Spiny Terrapin, Turquoise Turtle
Wasp:
Amberbarb Wasp, Bloodsting Wasp, Twilight Wasp, Wood Wasp
Wyrmling:
Arcane Gorger, Mana Wyrmling, Shimmering Wyrmling, Untethered Wyrmling