243
Have hunted deer almost exclusively with a blr .243 from the time I was 16 until about 44 when my son laid claim to it. Don't know how many deer and antelope, but lots, at least 2/yr, sometimes more.
Early yrs. used mostly 87gr, tried up to 110gr. I believe now nosler makes a partition around 90gr. That'd be my bullet choice for deer.
Nearly all of my successful hunts were one shot, drop on the spot. A .243 is fast, flat, and very accurate.
Only once I had an animal run, a running antelope, aimed just behind the shoulder; when the bullet landed it's leg was back, and hit it in the bone just below the shoulder joint(shot a couple inches further fwd than intended). Broke the leg, but did not penetrate the chest. Luckily last shot in the clip did the job, but taught me a .243 lesson: chest good, neck good, shoulder bad.
If you go with the .243 I'm sure you'll be happy with it.