Exactly, Tom cat bait chunx with tamper proof bait stations. If you are seeing rats then you are inundated. Bait stations will clear them out nicely then it's minor upkeep, just a few chunx per station to the rodents from moving in.
Don't get me wrong, shooting rats is fun. It's just not going to put a dent in the problem. A good break open .22 pellet gun is nice to have around. I've used mine to dispatch mink, weasel, small raccoon, etc.
Hatsan .22 is good pesting gun. Not too heavy, not overpriced and good power for .22 caliber. JSB 18 grain domed would be my pellet of choice. Don't bother with a scope unless you purchase one that is made for these one pump rams. Even the gas ram which I highly recommend will destroy scopes.
https://www.airgundepot.com/hatsan-mod-95-vortex-qe.html#HC9522VORT