There are so many good ones that it’s impossible to pick “the one” for each category without second guessing. AT least the categories are easy enough to pick...well you can add subcategories or disclaimers...
Small game- .22lr is essentially a must, but 17hmr is usually more accurate and is devastatingly effective, even on sub-par shots.
Varmints- .223 is the go-to but it is far from the end-all-be-all round. If I could only have one it would be a 223, but one I’m longing for pretty bad is 20 practical. All the good about a 223 amplified, and all the marginal or bad gets left behind. Then you look a different direction and see a .357 levergun, and a 9mm carbine...
Medium game- here’s where it quickly starts getting trickier. A 30-30 is the historic king of the woods, and it’s no slouch, but a .308, 7-08, .243, 7-30 waters, 35 rem....... yeah, this category is crowded with great options, and there’s bleedover both directions towards varmints and towards large game. The 6.5 crowd is getting the limelight for now, but I still like the .277 to .308 bore rifles in most any flavor. I’m picking 6.8spc here as it is a great under appreciated round.
Large game- long actions and bigbores. Anything from .270 win up gets the nod. I especially look at the .338 and 35 cal offerings but some “exotics” are great too. I’m settling on a very popular round in Africa, .375H&H.
Dangerous game- when you pull the trigger knowing you Might need to rack a self defense round you know you need something dependable. .50bmg sounds like it’s a great option but it’s too heavy for quickly aimed shots, so I’m looking more towards one of the Nitro Express rounds.
Just to add a kinda silly range round that’s a lot of fun, 30 carbine. It’s a hoot to shoot with so little recoil. Too big for bunnies, not big enough for deer, not great for varmints, but lots of fun.