I hunt in the Southeast. Grew up in Alabama where the limit has always been generous. Up until a couple of years ago we could LEGALLY kill over 200 deer a year. I never killed quite that many. I now hunt in GA, AL, FL, MS, MT, TX and MI just about every year.
For the first 31 years of my hunting life I used a Remington 700 in 30-06 with whatever ammo I could find because that's the only rifle I had. Didn't make a hill of beans difference to me...or the deer. The cheapest thing Walmart, Kmart, or any other store had available. Some of it was FMJ from the 60's. I really couldn't count the number of deer I killed with that rifle. I occasionally used buckshot out of an O/U 12 gauge and once borrowed a friend's 7mm mag to take a deer.
Then I started buying guns.
I have a Rem 700 in 243 and never lost a deer. Most run a few yards.
Marlin 336 in 30-30 (2) I have killed quite a few with these guns and have never had one run more than 10 yards. Basic Rem Core-loct 150 grain.
Several other calibers and models of rifle in 30-06, 243, 7mm-08, 308, 35 Rem., and others have killed deer for me.
A few years ago I bought a Swedish Mauser in 6.5x55, had it drilled and tapped, put a Leupold on it, and turned it into my main gun. It has been perfect and two kids have taken their first deer with it. Recoil is similar to a 243 for me and I am not recoil sensitive. It likes the ammo I buy online, don't recall the name right now, and is not terribly accurate with the cheap PPU ammo I originally found for it locally.
I recently acquired a nice BAR in 7 mag but I doubt I will shoot it much. Price was right and I already have one in 30-06 so...what the heck.
I now hunt with one of four guns. The Mauser, Remington .243, Marlin 30-30 (rarely), and a Savage 30-06. The first three are all kid friendly which is what I am all about now. All of them have decent quality optics, $200-$300 except the Marlin and it has a Bushnell that was cheaper.
Bullet placement FAR, FAR outweighs all other considerations for whities. I am living proof that caliber, model, bullet type, etc take a backseat to where that bullet enters, and hopefully exits, the animal. Whitetail just are not that difficult to kill. They are extremely durable but the kill zone is pretty large and the bones are not so big that they cause big problems for most "deer calibers". It is really rare that I have made a quality shot and had the animal run more than 25-30 yards and they generally don't run at all. Of course I haven't taken a shot over 150 yards in 15 years. Virtually every deer I have had to track, whether I shot it or someone else, was due to poor shot placement. There are exceptions, I had one this year, but they are rare.
Know your gun and know your distance. Don't take stupid shots at running deer. Those usually lead to heartache for you and the deer.