I like a 44Mag from S+W or Ruger.

Illinois law requires the handgun to be at least 30 cal, and have at least a 4 inch barrel. It also requires the ammunition to be at least 30 cal and be able to produce 500 Ftlbs at the muzzle as published by the factory, and must be of the expanding type.

I didn't have time to read the regs posted above, but if they are similar to IL, watch your 357 loads. Some may dip too low in power. They are the bottom end for deer.