Unless you are towing a Mack almost any 1/2 ton pickup will be more than enough to tow vehicles from an auction...
As long as it is a 1/2 ton that was set up for reasonable towing capacity from the factory, i.e. tow package, integrated receiver hitch & wiring, etc. The size and type trailer you are considering also comes into play. If you are talking enclosed you may well need a 3/4 ton. Flatbed with two axles? Tow bar? You could probably use a V6 Ranger and pull a car from an auction once a week.
I owned a 1996 F150 SuperCab 2WD with a 351, E4OD, and a limited slip diff and it would just about tow anything I ever contemplated with ease. This truck is still seeing daily commercial use in Rochester, NY, and because of the 1st decade of use being in the PacNW (no salt) is one of the few of its era I've seen back there without body rot.
Finding one in your neck-o'-the-woods might be a challenge, though.
Trucks, Suburbans & Tahoes, Expiditions, etc. were (originally?)designed to work. If equipped with factory towing capability they'll be more than capable for "weekly towing". I would hate to imagine how many SUV's & 3/4 ton trucks never even had anything bigger than a U-Haul trailer attached...
Cheers!
p.s. "Mid-priced" is a term that means different things to different people: $20K is mid-priced to some and probably won't get you a low mileage 2004 Escalade, either.
But it surely can buy one heck (are we allowed to say "heck"?) of a used truck, especially around here!