At the $20K budget level, you will be looking more for something in good shape rather than something with specific features or a specific model. In other words, you can't afford to be fussy.
Remember, a longbed truck can haul any camper, but a shortbed can't.
Also, cab length is not relevant when it comes to hauling a camper. Regular, extended, or crew, doesn't matter. Sure the extended cabover campers might look a little funny on a regular cab truck, but they will still work fine.
Shortbed campers are a fairly recent development, and have only become common in the last 10 years or so. You will be looking at older campers >10 years old in your budget range, so assume you're going to end up with a long bed camper.