I assume that by proscenium you mean proscenium opening?. There's no standard size Sean, it depends on the height of the booth and the height of the performer. The top of the proscenium opening is more or less the top of the booth. In the case of a hands-above-head fit-up and a standing performer the playboard is usually an inch higher than the height of the performer. Therefore the height of the pros opening is the height of the booth less one inch, less the height of the performer.
Actually at 3 foot your opening is wider than the norm, since most portable booths are only 3 feet wide so the prosc opening width is usually less.
The considerations apart from your height, method of operation, and height of booth are the proportional appearance of the proscenium and the height of your Punch (or tallest puppet).
Aesthetically, like a picture frame, the proportions of height to width should look pleasing. Traditionally prosceniums for comedy theatre are high and narrow while tragedy is served best by a much wider proscenium.
But the actual shape of your opening can be disguised by the shape and proportions of the proscenium Surround.
There are many, many prosceniums shown in the photographs on this website (especially in the Festivals gallery). There's nothing to stop you having a look, and maybe even using a ruler to measure the various widths and heights - and scale up (guided by fact that many booths will measure 36 inches across) - to give you an idea of the variety of sizes which, I would guess, will fall between 17 and 22 inches.
Remember a very big elaborate proscenium dwarfs and draws attention from the puppets, whereas a smaller opening and a simpler surround does flatter the puppets. However the huge, elaborate pros does look impressive between shows at a public event.
These matters are discssed on the website - in Prof Punch Tips - article entitled
Designing a Proscenium. This has pictures of various prosceniums with comments.
http://www.punchandjudy.com/prosceniums.htm
You might care to take a look.