I've read and Heard from different behind the scenes of The Muppet Show that full body puppet characters like Thog has a small TV inside so that the puppeteer can see what he was doing outside of his costume. Does anyone knows what kind of models available on the market for amateur productions?

This is one I have been debating on.  My thinking is a webcam, a tablet, and an extra power source.  Not sure how to properly connect, but that seems to be the best and lightest way to do it.  And re-reading, are you are talking about actually seeing your character move on set or being able to better see while in costume? 

I was thinking of both parts. I also read on the Season 1 DVD text-commentary that some full-body puppets have hidden eye-holes (possibly very thin fabric that you can see through but still hide your eyes and face) so that Jerry Nelson could see out of his costume (unlike Frank Oz when he did his only full-body puppet as The Choy Dragon, which didn't even had eye hole which made a living hell for him and henceforth refused to do any full body puppeteering, maybe the main reason why he had a hand puppet for the Sweet Ginger Bread man number). Your idea of using a tablet might and webcam might work but I wonder if maybe an Android/I-phone would also work, making it even more lighter, if it's possible to connect a cellphone to a webcam.
Slightly out of topic I was thinking that instead of using TV sets in order to see the puppetry, you could use laptops to watch your movements, being connected to the cameras. Wonder if that will work?