Pesty,
I use a 25 cal Marauder rifle with an ATN X-Sight II HD 3-14 optic. I originally got the Marauder with a Hawke Vantage 4-12 x 50 scope for my ground squirrel problem. The Marauder and JSB Exact King .25 pellets made quick work of the ground squirrels.
The Marauder pistol or rifle will work for your rats, the price range you are trying to work with may not!!! Air supply equipment and other necessities will push you past or right to your budget limit.
I use a Hill hand pump and find if I top off my reservoir after a magazine to be doable. Depleting the reservoir and then hand pumping becomes a real chore for me, old guy limitations.
I shoot rats from stacks of firewood near my workshop and equipment sheds at 15 to 20 yards. All i need is a head to poke out from the firewood, with the glowing eyes it is easy to get a good clean kill shot. The Marauder and ATN do an excellent job, the rest is up to me, I have made myself a concealed shooting position, comfortable shooting stool/chair and an adjustable Primos tri-pod and I can sit for hours waiting to ambush the rats.
Good luck with what ever you decide to go with and have fun.
Claude
