If there was a variant for different types of shields, how many types would you do (2? (light and heavy), 3?(buckler, light, and heavy), 4?, 5? 10?) and how would you balance them?
I would do a few types of shield, but I wouldn't change the AC bonus. Every shield would give you the same 2 points to your AC, but that bonus might become situational based on the type of shield.
For example, a buckler could give the same AC bonus as a regular shield, but apply to only one attack per turn (or 2 attacks if the wielder used a reaction.) The benefit would be that it was lighter, and would allow the user to hold an object in their shield hand or to use that hand to execute the somatic component of a spell or load a hand crossbow.
For the crossbowman's shield mentioned above, the shield could be a normal shield until it was set down, then it would give its bonus only against attacks from 10' or more away, and only from the front arc of the crossbowman. The crossbowman could pick it up and move with it, setting it again after the movement, but would be limited to half his movement. The advantage would be that both hands would be free to load the crossbow.
So I would balance the shields by keeping only one shield bonus to AC, and giving any variant shield benefits and limitations in other areas.