For $300 you will have to be looking used or you will get an average at best picture taker.
Look into an older model Canon or Nikon DSLR. Nikon's usually can be had for a little less then a comparable Canon model. The mirroeless systems can also be had at a good price I would prefer Sony here as they have more lenses on the e-mount than the Canon or Nikon mirorless bodies.
This is something that would work for you in your budget.
Please view this ad:
Sony A3000 Mirrorless Digital Camera with 18-55mm Lens,
https://www.kijiji.ca/v-camera-camco...nt=app_android
May want to upgrade to a longer lense for wildlife but is a good start and takes any E-Mount lense (options are wide open for new glass). When buying remember bodies come and go glass doesn't spend the money where it counts (lense).