To unlock the following suits for Iron Man to use, complete the requirement listed.

Suit	How to unlock
Classic	Complete the challenge "One Man Army vs. Mercs"
Classic Mark I	Complete the challenge "One Man Army vs. AIM"
Classic Mark II	Complete the challenge "One Man Army vs. Ten Rings"
Classic Mark III	Automatically unlocked
Extremis	Complete the challenge "One Man Army vs. Maggia"
Hulkbuster	Complete the challenge "One Man Army vs. AIM-X"
Ultimate	Complete Story Mode in its entirety