Godspeed my friend. Recently went through the truck search.
In the 250/2500 and 350/3500 arena you have 2 things in the under $20k price: 1) Old trucks with tons of miles or 2) Hot rodded/lifted trucks with lots of issues. Even bumping the price up to $30k there are some deals but many will have miles or have obviously towed their entire life.
In the 150/1500 space it's a little better but even then the same rules seem to apply.
It took me 6 months to find something decent and in the budget. Although I was only searching for Fords. But I imagine the same applies for all the makes.