Corefire Imp is of the Humanoid family, but wields mostly Elemental attacks, with a few other types thrown in:
For the first slot, you have a choice between Burn and Rush, the former making him very strong against Mechanicals, but weak against Critters. Rush, on the other hand, is strong against Critters, but weak to Flying. Humanoids take less damage from Critters, so Rush turns into a very good choice overall, allowing the imp to go first the next turn as well.
The second slot abilities have DoT elements, and that is where Corefire Imp really shines. When either ability hits, he will gain health every round, effectively turning these DoTs into HoTs. Which ability you choose will depend on your overall strategy. The Immolation DoT lasts much longer, but has no initial damage, whereas Flamethrower has an upfront burst and a shorter DoT. Neither have cooldowns, so go with whatever suits your strategy -- using Flamethrower is a more aggressive, fight-to-the-death move, and Immolation more useful for long-haul battles.
Choosing between Cauterize and Wild Magic is also very dependent on your battle strategy. Cauterize is a very large heal, and will keep your imp in the ring quite a while, paired with his DoT abilities. Wild Magic may seem iffy, but take a closer look. It adds damage to every attack, and the attractive pairing with Immolation may turn Wild Magic into your third slot choice. Although the Immolation/Wild Magic combination is very strong, keep in mind that without Cauterize you should take a more cautious approach, switching the imp to the back line while it heals up through the Humanoid passive.
Overall, the tanky combination of damage over time attacks and heals makes this Humanoid battle pet a nice option for your battle pet toolbox. Have you farmed up your Corefire Imp yet?