I'm making a 3rd person shooter game. I want the player's weapon to follow the mouse. How many animations would I have to do to achieve this?

hello?

You won't have to use animations for this, you can use the ent_bonerotate function for that. Otherwise you'd have to create a massive amount of animations for this

Edit:
for just rotating the player though you wont even have to do that, you can just use c_rotate with the mouse vector. I thought you wanted to rotate up and down, that can be achieved by using ent_bonerotate