Rock head would probably put it in the OU teir. It has lot of recoil moves. Also tough claws could be a good ability.
Arcanine has a lot of good qualities, and his abilities are one of his better aspects. Sure we can just give him a super overpowered ability and that'll make up for all his other issues, but that feels less like improving Arcanine and more like just turning Arcanine into anotherpowerful Fire type. It feels kind of lazy to me. Arcanine's abilities are one of his strongest points.
Here's what I would do to Arcanine:
Bump up its Speed, for a start. It's just holding back the poor guy so much and it makes it a lot harder for him to be a threat. Maybe give it a bit more bulk, though his abilities already help with this somewhat.
Change its typing to take neutral Stealth Rock, too. Fire/Steel doesn't really make sense, and I'm assuming flavour is something we want to factor in (i.e. he's not getting hydro pump).
Fire/Ground has potential, the trade-off being a 4x Water weakness, but that's all it loses there. We could probably do with giving him Earthquake or something if we want to do that.
The last option is Fire/Fighting. You could probably make a case to justify a Fighting-Type Arcanine flavour-wise, as the Fighting-Type represents heroic Pokemon, not just punching/kicking/whatever fighters. Arcanine looks pretty heroic too me, but it is a stretch. Think Coballion, Keldeo, etcetera. Anyway, a Fire/Fighting Arcanine loses the Rock weakness, but gains Flying and Psychic.
So yeah, I'm voting no new moves or ability. But if we choose to change the typing to Fire/Ground, we should get the option to give it some Ground-Type moves even after this stage. I personally think we should have voted on the typing first, doing it this way doesn't make much sense to me. The typing immediately tells us what will threaten Arcanine and what we need to be able to deal with.
Tough Claws
One of Arcanine's issues is the fact that offensive sets are outclassed by Entei, as Entei is faster, bulkier, and stronger than Arcanine. Tough Claws remedies this issue somewhat by boosting the power of every move offensive Arcanine uses, such as Extreme Speed, Flare Blitz, Wild Charge, Close Combat, and Crunch, by 1.3x. Fortuitously for Arcanine, this boost stacks with Life Orb, making Arcanine an obscenely powerful wallbreaker. Suddenly, Arcanine's Wild Charge can now 2HKO the most physically defensive of regular Slowbro, while Extreme Speed is boosted to the extent where Arcanine can act as a fantastic revenge killer. Even the humble Stunfisk, which, while not viable in OU, completely walls normal offensive Arcanine, is now easily 2HKOed by Flare Blitz. Tough Claws is better than Reckless because it boosts
all of Arcanine's physical moves... not to mention that it boosts them to a greater extent than Reckless (1.2x vs. 1.3x). It is also better than Rock Head as Arcanine is not exactly the sturdiest Pokemon, meaning the benefits of incurring no recoil damage from its moves are outweighed by the negatives of losing switch-in opportunities afforded by Intimidate or Flash Fire.
Of course, Tough Claws is balanced out by the fact that Arcanine's recoil moves now kill it much more quickly due to their increased damage output. Furthermore, it does nothing to solve Arcanine's issue with every entry hazard, particularly Stealth Rock.
My issue with this is the same thing I've been saying. Sure, a new ability makes Arcanine tough, but I just don't feel like it's the right way to do it. Abilities are one of the few things Arcanine has over Entei, it makes more sense to me to just fix Arcanine's SR weakness and buff his stats a bit.