You’ll want to go .25 at a minimum and and you’ll want to go PCP. Consider the new Hatsan Carnivore in .30 or .35 cal. Good shot count, great accuracy, and plenty of power. If you are wanting to stay with a spring or gas ram gun, then you need to have reasonable expectations on what game you can take. Turkey is ok.. but the other animals you mention need more power for a clean
If you have a standard home shop compressor then no. You need to get to 3000 PSI (for most guns). Most home shop compressors, or even the commercial garage compressors, top out at 150 to 165 PSI. Cheers AGWTV