I am a beginner on a limmited budget. I am hoping to build another puppet using wire for the armature. I must use a webcam, so my project can't be too large. What dimensions should I make my puppet so that it is easily manipulated but also clear on my 1.3 MP webcam? 

Are you talking clear as in a focus standpoint or quality standpoint?

The image quality standpoint.

It's mostly a trade-off between several things - the space you have for your set,  what is a good size to animate, whether you need to use existing objects in your set.  Which camera you use isn't as important for puppet size as getting puppets that work. I use the same size puppets whether I'm shooting standard def video (PAL 720 x 576 pixels), 35mm film, Hi Def, or with a 6 megapixel Nikon DLR still camera.

8 to 12 inches tall makes a good puppet for animating.   Too big, like much over 12", and the weight of the puppet makes it harder to hold a pose without making it stiff and hard to handle.   (And the sets can get really big too.)  Too small, like much under 6 inches, and every small move you make is magnified and seems bigger, so it's hard to get smooth animation.  It's also harder to get good detailing on puppets and props.

I think Snoutley (my avatar) is about 7 1/2" tall, with a lightweight body of cushion foam over a wire armature.  He seems to work pretty well.  He's meant to be a short gnomish dude, so I use him in a 1:6 scale set with my 12" humans.   

My latest puppets are about 4 inches tall. Bigger than tiny lego people, but smaller than most puppets. I choose this size so I can use less material in the puppets and sets and so they will not destroy the foam core set floor when they are tied down.