I have used several different rifles and shotguns with buckshot. I have killed around 100 deer. I wouldn't use anything less than 30 caliber from my experience. My best deer killing rifle is a 300 Wby. Every deer I hit with it I retreived. I have had 2 travel out of their tracks. The others just fell.
I have hunted every day I could during deer rifle season my whole life. I have hunted with a lot of people shooting everything from 22 Hornet to 340 Wby
I have helped track deer other people shot for 40 years. Deer shot well can go 300 to 400 yards before they bleed out and stumble and fall. In my experience a 30 caliber will bleed them enough to find them. Some of the smaller stuff works to kill them they just don't leave a big enough hole or exit to bleed and leave a trail. It makes finding them more difficult than needed. I realize many people like their smaller caliber rifles, I just don't think they are best. If I had to pick one it would be a 30-06.