First, get two rifles with scopes, one a .22LR with the same action and close to the same feel/safety location/operation as the centerfire. Scopes take most of the poor sighting situations out of the picture because the target and sighting planes are the same. A 3-9x variable is optimal for most hunting situations out to 300 yard. (I can't recommend shoot beyond 200 yards until you've killed a dozen deer at closer ranges.)
Fire the .22 until you feel comfortable hitting the 9" paper plate in the center 3" with every position you intend to use in the field. Prone isn't usually a good position, but sitting, with or without a rest; standing, with or without rests are common field positions. When aiming, look at the target center and not the reticle. If you do that, you'll see the reticle with your peripheral vision and naturally guide it to the target center.
At whatever range you can hit the 3" in each field position, keep that in mind and practice determining that distance in all hunting situations, including a half-hour before sunset (or sunrise). That's your baseline point-blank range and should account for a bit of buck-fever, numbness from the cold, etc.
After all that is accomplished, practice with the centerfire rifle to achieve the same results. Keep practicing with the rimfire, shooting at least 100:1 over the centerfire and you'll increase your point-blank range in perhaps a half-dozen range sessions.
For at least the first few years, consider shooting from a blind, with something to rest the forend of the stock on. Finding a good place to wait for deer is the trick, but that's another subject.
Note: I started shooting at about 7 yrs old with my brother's BB gun and wore out that one and two more because I loved shooting and was pretty good at it. At 67, I still shoot a lot and very much enjoy offhand shooting.