well i want to ask you people about something. What are some good varmint/predator rifle and handguns for about 350-400$? like can a 22Lr/22mag single action do the varmint(FL varmints coon-bevers) job and which is better for predator a bolt, auto, or single shot like a H&R and what about a 20ga for coyotes or a 12ga? also what about a laser on a hundgun or 6 shooter for fast shots.
My varmint gun; a 375 H&H Magnum using Hornady 300 grain FMJ round nosed bullets. It will put 3 of them into less than an inch at 100 yards off the bench. The Jackal was taken at night with a spotlight.
Since the targets are small, the first consideration for a varmint gun is accuracy; the particular cartridge you choose isn't that important as long as you use it at the ranges for which it was designed and place the shots well. Since you'll likely only get one shot before the animal vamooses, you don't need an autoloader. You shouldn't be counting on "fast shots" with a handgun to net you anything other than air at other than very close range unless you plan to invest several hundred dollars in handgun practice ammo.
Unless you shop for a used gun, your budget is probably only going to buy you a rimfire chambered firearm. If I were working with your budget, I would look for a good used .224 caliber centerfire rifle with a scope. There are people that buy guns and tire of them whereupon they trade them in on a new toy before their first gun is even broken in.
A shotgun would work fine for your intended purpose at ranges up to 40 yards as indicated above. A shotgun would not be my first choice in a varmint gun.
