I have compiled a list of the best costume cores for each hero. The first assumption is that this is for optimal performance; special item find and rarity increases are excluded.
The second assumption is that certain statistical thresholds are more valuable than others, based on the abilities they confer. I've identified the key stats as Durability 6, Strength 6, Fighting 5 & 7, Speed 6, Energy 7, and Intelligence 7. After each recommended core I will list the value to which the core would raise that stat.
Feedback welcome.
Black Panther: Fighting 7
Black Widow: Fighting 7
Cable: ??? I don't have Cable's final stats; please supply if you do.
Captain America: Strength 4/Energy 2 Cap is one of three heroes without a good option. Strength would boost damage; energy would remove energy and mental damage penalties.
Colossus: Fighting 5
Cyclops: Energy 7
Daredevil: Fighting 7
Deadpool: Fighting 7
Hawkeye: Fighting 7
Hulk: Fighting 5
Iron Man: Energy 7 seems obvious, but Tony could also reach Speed 6 to boost attack speed.
Jean Grey: +Spirit? Jean has no good choices among the six primary stats.
Ms. Marvel: Strength 6 (melee)/Energy 6 (range) The strength increase enables your melee powers to stun; I haven't played her so I don't know how difficult this choice is.
Punisher: Fighting 7
Rocket Raccoon: Fighting 7 assuming his powers are classified as Fighting Powers; take Energy 6 otherwise.
Scarlet Witch: Energy 7
Spider-Man: Speed 6
Storm: Energy 7
Thing: Speed 3/Energy 2 He's in a similar boat to Cap, but can go for a +5% movement speed increase.
Thor: Energy 7 (range)/Speed 6 (melee) Energy is likely the more valuable bonus, but I haven't played him so I don't know how difficult this choice is.
Wolverine: Durability 6