The normal recommended minimums for raccoon would be something in a .22 or .25 airgun with at least 25 FPE. Some people would tell you 35 FPE but at that power level, you're getting into PCP's and above your $300 limit. For under $300, you could look at a Benjamin Trail NP in .25 caliber. It's a single shot, gas piston, single cock airgun that takes 47 #'s of cocking effort. You'd be a little below what's recommended for chest shots but right there for head shots. Preferably in the ear. Hopefully this helps narrow it down for you.