Plastic ukuleles were all the rage in the 1950s. They were much cheaper and quicker to produce than wooden ukuleles and, largely thanks to the endorsement of Arthur Godfrey, sold by the barrow full.
Of these designs, it was Maccaferri who had the most success. Maccaferri were, and still are, most associated with their jazz acoustic guitars as used my Django Reinhardt. The Maccaferri Islander ukulele was a big success. As well as the soprano model, they also had a baritone Islander which mimicked the distinctive shape of the Maccaferri guitars. One thing you might like to keep an eye out for whilst perusing Maccaferri ukes is the color. Most of the ukes had a plain white front, but a range was made with a pearl effect front.
Also very popular, thanks to Arthur Godfrey's endorsement, were Emenee's Flamingo ukulele. These ukes came with a set of pitch pipes attached to the headstock. I'm not quite sure how you're supposed to tune your ukulele whilst playing these pitch pipes, but it certainly looks great.
Both the Islander and the Flamingo came with a button operated chord device that straps over the neck of the ukulele (called a Chord Master on the Maccaferri and a Uke Player on the Flamingo). The device was originally patented by Mario Maccaferri (you can see it here). Having one of these adds to the value of the ukulele.
As well as making the Islander, Maccaferri also produced the Mastro TV Pal and Playtune ranges of plastic ukes. Maccaferri ended up selling his rights to the Carnival company.
Other plastic ukuleles you are likely to come across are the Lisa, the Fin-der and the Mauna Loa which bear an uncanny resemblance to each other and most probably manufactured by the same company.
As well as Arthur Godfrey, there were plenty of other celebrity plastic ukes, including a Beatles ukulele (by Maccaferri) and a Ukulele Ike uke.
If you'd like to learn more about the history of plastic ukuleles, I can highly recommend John King's article.
Gus of GUGUG guides us through his extensive collection of plastic ukuleles.