Fun!!
Every varmint hunter needs a .223
I'd throw in a good 6mm for varmints, since that's where a lot of my personal hunting opportunity is... I am a little partial to the 6BR.
A good mid caliber for plinking/practice at long range... 6, 6.5 or 7mm... so 6 or 6.5 creedmoor maybe, or .284 win? I like to see a little bullet splash, and traditionally 6.5 Creedmoor is easy to obtain, easier to see splash than a 6mm, easy on us soft shouldered folk, so let's go with that. Also makes a decent deer rifle at most of the ranges I get shots at. Don't hate!!!
Good hard hitting 7mm or 30 cal for hunting long range... 7 mag, 280/ai, 28 nosler. Or 300 win mag, 300 rum, 30 nosler, etc. I personally have always had a fascination with the 28 Nosler. Zero personal experience and mostly out of my budget for a "luxury" gun, but hey, it's MY list, so we will go with 28 Nosler.
I'd have to top it off with a 338. Had an Edge once, found it would be difficult to mag feed. So I'd either go with one set up for that already, or (likely) a different cartridge. None in particular. Lets say lapua for the sake of argument.
There you go, the definitive list of 5 "best" cartridges