I concur with the above calibers. I chose a 243 for my vermin gun. I will get a 223 soon as I can talk the wife into it. I recommend a bolt action. Most makes are accurate and dependable. A few to look at: Ruger M77, Remington 700, Remington 7, (youth size) Weatherby Vanguard and Howa, Winchester 70. Lots of other choices but these are the ones I have experience with.
You can't fix stupid....however ignorance can be cured through education!