So for squirrel head shots you need a rifle capable of 3/4" groups at whatever distance you hunt them. You also need to deliver at least 4 foot pounds of energy at that range. Stay away from ultra light pellets, they do not carry the energy needed to cleanly take game at any realistic hunting range. I also reccomend .22 cal or possibly .20 cal, over the .177's for hunting. As for $100.00 limit I think you should look to Gamo, RWS, and the lower end of the Beeman line. If possible try to actually hold and or fire any you are considering, stock dimentions being slightly different between the models. In .22 look for at least 800 fps at the muzzle WITH STANDARD WEIGHT PELLETS.
good luck, and have fun
Keith