Ice Minion - Best minion for attacks and blading/trapping because ice is the weakest school for attacks. Fire Minion - Because fire is between ice and storm, they made it mainly a minion to get rid of shields using link. Storm Minion - Since storm is the strongest school, they made it have the worst minion.
I can't vouch for others, but I have good results with the water elemental. Lvl 31 storm no-crowns player.
Out of hundreds of PvE street matches and some boss battles (krokopatra, grubb, Ngozi the Beguiler, etc.) I've lost many, but only one that I can recall where I had the minion out.
The key is once you recognize you're heading into a slow spot, when your first and second attacks fizzle or are weaknessed, sprite yourself then cast your minion. Or tower up then cast minion.
It takes him a while to get himself set up. His logic says to shield himself, taunt, heal/shield himself, taunt, etc. That's what he's there for. All you need to do is survive until he starts to taunt. Sometimes that's no easy task.
But do not make the mistake of waiting until you're low and then casting minion with your last pips, and hoping he will heal you. I can count on the fingers of one hand the times he's healed or shielded me instead of himself, in all the pve matches since Nightshade.
For those first 3-4 turns after you cast him, you are on your own. Pretend he doesn't exist and just take responsibility for yourself. You can do this a lot better if you pre-emptively tower up or sprite up before casting him. and you really need to use your time wisely when you've recently cast him.
You still get the occasional storm trap, spirit armor, elemental shield, or sprite that you otherwise wouldn't get.
So for those of us who haven't managed to breed a pet with spritely or unicorn yet, water minion is still a strong second choice.
I don't do PVP but I do know that killing enemy minions is pretty important...storm minion is hard to kill and seems not a threat at first, so people may be likely to leave him around to do his occasional thing. If you can manage to drag the match out really long the small things he does to mess with battle plans will add up.