An entry-level handgun powerful enough to hunt deer is not an entry-level handgun, in my opinion.
You're looking at a .44 magnum Ruger Redhawk or Blackhawk, Smith 629.
But to me, a .44 magnum is a poor way to get into handgun shooting. They have a relatively steep learning curve to comfortably shoot when it comes to recoil and ammunition is harder to reload for than standard-pressure handgun rounds.
I'd consider starting with a nice .357 magnum with a six-inch barrel. It will definitely be effective against black bears. You can hunt deer, but it's certainly not an ideal caliber for the task.
Two cents. And have fun!