For coyotes and deer the 243 would be about perfect, but you could look into the 6mm Remington, 25-06 or 257 Roberts as well. If you plan to be a fair weather hunter/ shooter I’d recommend a nice wooden stocked Remington 700 BDL or CDL, a Winchester Model 70 Featherweight or Ruger 77. If you want something a little more durable to the conditions you may encounter outside, stick with the same models but look for ones with a synthetic stock and stainless barrel.