I speak as someone in the firearms industry.
For whitetail size game, and getting into it now, get a .308. Many/most hunting calibers are hard to get and we are still another/one more event away from another ammo scare. The .308 is a fine choice and it is the most readily available centerfire ammunition available right now for deer sized game. Sometimes, the times and ammo availability influence the recommendation. I see 20-30 people a day looking for ammo for their hunting rifle that they cannot find. I have thousands of rounds of .308 in stock including hundreds of boxes of .308 hunting ammunition.
Savage, Ruger, and many others are absolutely fine for entry level rifles, and if your budget allows, there are many fine $1,000+ rifles out there in the "buy once cry once" category.
With a hunting rifle setup, do not make the frequent beginner mistake of having tunnel vision on the rifle. The optic you put on it is just as important. I am optic quality biased, and I would actually say the optic is more important than the rifle. Modern budget rifles are capable of perfectly acceptable accuracy at under $500. I would prefer a $300-$500 rifle with higher end optic than a $1,000 rifle with cheap optic. In whitetail deer hunting especially, that first 30 minutes and last 30 minutes of legal shooting time seem to have a lot of activity. A quality scope with high end lenses and lense coatings will allow you to clearly identify and take the shot. You will not be able to do that with a bargain basement scope.
This is likely controversial, but I absolutely disagree with the advice of a 22LR bolt action with iron sights. That is like the old school advice of learning to drive a stick shift first. It is outdated and misguided. If you want to learn how to shoot and hunt deer, learn how to shoot a bolt action with a scope, and you can do that with the rifle you will hunt with.
