There are some units that new people probably dont really understand, some of them can be quite tricky. I'll add some of them here and anyone else can add other ones I leave out.
Age 2 greek cav unit: called Sari, is a cav unit that deals pierce damage. This unit counters ranged units,
Age 3 unit: Mounted archer (MA) (babyloanian and persia units): This unit is an archer that sits on a horse, so they appear to be a cav unit. However they are considered a ranged unit, they also do pierce damage and counter cavalry units. Spearmen do not counter MA, because MA are considered ranged. Slingers, and pelts are some units that counter them. (sari also counter MA, but MA counter sari also)