Look for centrifugal aerator pumps. They're the cheapest to operate. It's really not a big deal to aerate 125gallon shallow tank though. I'd probably just put one of those hang over the side type filters on it to move the water and help filter out solids. Unless you put a bunch of minnows, like over 100 saltys or 200 fatheads...keeping the the water agitated with a normal 10 gal. aquarium sit air pump should be fine.
Years ago I had two 10" crappies and about 15 fatheads in a 30 gallon feed pan for over a month with no air and only rainwater replenishing it.
"The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge." Stephen W. Hawking