Can we have two?
My cheapest GREAT gun has been my CVA Accura V2. I got mine on sale and remember it was like $280 or so. I spend more on black powder "supplies" (like patches, bore lube, etc) but having done that it's a very cost-effective system. More important, muzzleloader tags are sort of a worst-kept secret where you can often get into premium zones with a fraction of the points you'd need for a rifle tag in the same zone.
My greatest CHEAP gun has to be my Ruger 10/22. What a performer. 100% reliable, easy to learn, great for kids and adults to learn general firearms use, trigger control, and so on, and I've taken squirrels, rabbits, grouse, the odd prairie dog, etc. I've never done it myself, but I know folks who with good shot placement have taken coyotes and hogs as well. And what a cheap gun to run - if you wait and watch for deals you can still get 500-round "bricks" for <$40. And name another round that can be bought in 1400-round "pails" for fairly short money...