Most people who have a computer that can handle play with Huge unit size. It makes the game feel more epic. Battles in antiquity where often very large affairs and Huge unit size comes the closest to depicting those epic battles.

There is no official recommendation on the size of units. Suffice to say use whatever size your computer can handle with a decent level of performance. I use huge and only get problems during bridge battles when the fps goes waaaay down.

On Large unit size there are few problems if you upgrade your cities infrastructure. On Huge you may have problems finding enough troops to recruit. Especially in the early game when you have to crank your taxes up high. The AI dosen't have this problems as they get scripted population assistance whenever they recruit a unit. Different amount depending on what unit size is chosen.

There is no difference in battle performance. The only difference is that on Huge settings the battles sometimes last longer. The only thing affecting battle performance when changing unit size is that some formation minimods are specifically designed for a certain size setting. And using a different one can have weird results for the AI deployment.