Armor research works in the same way as weapons research, though the various types mean there is no “best” option. Go with what works best for each individual class or character and the role you’ve created for them.
H = Health Bonus
Salvaged Alien Materials, 10 alien alloys
Unlocks: Carapace Armor (H:4), Alloy S.H.I.V.
Carapace Armor, 15 alloys
Unlocks: Skeleton Suit (H:3, grapple hook, increased movement)
Carapace Armor, 15 alloys, 5 Elerium
Unlocks: Titan Armor (H:10, poison immunity, flame immunity)
Titan Armor, Hyperwave Communication (see “other”), 15 alloys, 15 Elerium
Unlocks: Ghost Armor (H:6, Ghost Mode ability, grapple hook)
Titan Armor, New Fighter Craft (see “other”), 15 alloys, 15 Elerium
Unlocks: Archangel Armor (H:8, flight mode)
Ethereal or Sectoid Commander interrogation, 10 alloys, 10 Elerium
Unlocks: Psi Armor (H:6, Will increase of 30 for psi attacks and defense)