To intentionally misquote the Bard, “Every stage is a world!”
At least in my book.

Backstory: For the past couple of years, I’ve been writing the occasional Punch & Judy script and coming up with various show ideas all based on glove puppets. In that time, I’ve become well acquainted with P&J-style booths (I built one) and performing (practicing, really) with my hands “in front” and looking through a scrim.
As I’m experimenting with “Muppet” style puppets (mainly Project Puppet's Simple series), I’m wondering if my P&J booth design is appropriate. I know I’ll have to build a bigger stage, but
I wonder about what kind of stages that puppeteers using mouth puppets use. Do mouth puppets work just as well while the puppeteer looks through a scrim (standing)? Or do most of you work with your hands over your head (a la Henson and company or traditional P&J)? I know there are advantages and disadvantages to both methods.
My personal preference is to perform with my hands in front of a see-through scrim. I know that it limits my character's range of movement, but the ability to see the audience overrides the movement limitations. I also like the "look" of a booth-style stage.
Now, this is for a solo show, but there's a chance that in the future I'll be working with other puppetteers on stage in a kids' show at my workplace (large chain bookstore). In that case, I'll be thinking more about working with the hands overhead and sitting on a rolling stool. That project will be dealt with later.
I'm sure that there's no "correct" answer to this, but I am curious.
Regards,
Rob