Welcome to Puppets and Stuff!
When do you get the puppets you are going to be using? As soon as you do start working with them in front of a mirror to see how they move and so you can become comfortable with them. As an actor you should have no problem with the multiple characters. It is the same with puppetry really as with straight theater. You develop your character based on voice and body language. The only difference is that the body language is that of the puppet.

That is why working in front of a mirror can help. You can catch things in how you move the puppet that helps define the character.
One quick tip that non puppeteers do not often realize is that your puppets lower jaw moves not the top of the head when they talk. Hold your hand up and like it is in the puppets head and try moving just the thumb which would be in the lower jaw. This is actually an exercise you can do before you get the puppet. Your top fingers may move some but you don't really want them to flip up. If you envision eyes on top of your hand you'll understand why you don't want to do that. If you did the eyes would be looking at the ceiling when they talk instead of the audience or other performer.
When I preform cabaret style like Avenue Q is presented, I try to not pull too much focus from the puppet. As a rule I look at the puppet I am preforming. They are an extension of me. That being said the director may have other ideas about that.
