PSP 1000
As the original PSP, the PSP 1000 (also called the "Phat") is the most likely PSP console to be found for under $100. Many video game stores and auction websites carry the PSP 1000 for as low as $70 for a used machine.
PSP Slim and Brite
The PSP Slim and Brite are somewhat less likely to found for under $100, but it is not impossible. Many of these PSPs found for less than $100 will be slightly damaged, needing replacement parts like a new screen or button pad. These fixes are actually quite cheap, and you can still end up paying around $100 for a device, in order to get it completely working. However, sometimes great deals do happen, and auction sites are the best place to find these PSPs for under $100.
PSPgo
The PSPgo console is the least likely PSP model to find for under $100, but it is still possible. The PSPgo originally retailed for $249.99, but because the public didn't receive it positively, Sony dropped the retail price to $149.99. This means used systems for under $100 are just around the corner.