I've stoned a number of wild pets, for a variety of reasons. In general, stone the ones that have unique (or super long) spawning conditions, or ones where you want a particular breed and finding that breed alone, much less a rare of it, would take excessive time.
As for me, this is what I stoned, and why.
For rarity reasons, Wanderer's Festival Hatchling, Baby Ape, Minfernal, Unborn Val'kyr, Scourged Whelpling, Giraffe Calf, and Crow.
For right breed (with too many options) reasons, Qiraji Hatchling, Flayer Youngling, and Sporeling Sprout.
For "I need you for a tamer fight RIGHT NOW" reasons, Tolai Hare Pup and Infinite Whelpling.
For "oh my God I'm so sick of farming you" reasons, Anodized Robo Cub, Cheetah Cub, Hare, Oily Slimeling, and Twilight Fiendling. (Other candidates from personal experience: Diemetradon Hatchling, Infested Bear Cub, Harpy Youngling, Scarab Hatchling.)
Groups 1 & 2 make for 10 pets. Groups 3 and 4 were last resort. I don't recommend others stoning either rabbit, for example. And I still mostly regret stoning the Robo Cub and the Cheetah Cub.
Edit: As for your list, I'd say wait on stoning that Grotto Vole, Death's Head Cockroach, Luyu Moth or Forest Spiderling. You'll want your critter, beast and flying stones for your non wild pets. Luyu Moths are plentiful in Krasarang Wilds. Grotto Voles and Death Head's Cockroaches can be found down the tunnel in Hyjal where they were holding Fandral Staghelm prisoner. They're both common as secondary pets in the Hyjal zone. I don't remember having an issue finding the Forest Spiderling either, but I'm also the person who stoned her Hare.
For the Arcane Eye and Restless Shadeling, do you do the tamer by Karazhan regularly? I see Arcane Eyes around her all the time. I think the competition for the Shadelings has died down, as I've seen them still up when I've done the tamer close to noon. Spend a weekend morning in the tunnels, and hopefully one will turn up.