There are currently 11 tiers of troop which are represented by Roman numerals.
Most commonly referred to as odd or even tier for explanation purposes.
The barracks need to reach a certain level to unlock the next tier of troop. These are as follows
Tier 1 = barracks levels 1-3
Tier 2 = barracks levels 4-6
Tier 3 = barracks levels 7-9
Tier 4 = barracks levels 10-12
Tier 5 = barracks levels 13-15
Tier 6 = barracks levels 16-18
Tier 7 = barracks levels 19-21
Tier 8 = barracks levels 22-25
Tier 9 = barracks levels 26-29
Tier 10 = barracks levels 30-33
Tier 11 = barracks levels 34 + 35
The higher tier is always stronger.
Odd tier infantry = raises HP 15% when you are on the defending side
Odd tier cavalry = reduces damage when attacked by archers by 25%
Odd tier archer = 25% bonus damage against mages
Odd tier mage = 30% bonus damage against cavalry.
Even tier infantry = reduces damage from mages by 25%
Even tier cavalry = raises attack when you are on the attacking side 20%
Even tier archer = 30% bonus damage against infantry
Even tier mage = bonus damage to all soldiers during city defence by 15%
These buffs only apply to that particular unit unless it says otherwise in its description.
You always include all 8 troops in all marches (other than gathering)