Why on earth would you be limited to only 10 rifles?
But, if for some arcane reason you are willing to only have 10, then consider the purposes of those 10.
You should have,
a .22lr. Any action style you like, but you should have one.
Centerfire varmint caliber. This can be anything from a .22 Hornet up to a .25-06, depending on your personal preference and how versatile you need. Bolt guns are the preferred action, but a good single shot is entirely acceptable.
Light caliber high capacity semi auto. What the anti's call an "assault weapon", for cover fire in a SHTF situation. Today, that means a .223. The Mini-14 does this. So does the AR, and the AK. The M1 carbine also fills this niche, but has less range. Has to be at least minute of man accurate at intended max range. If its better than that, fine.
Deer rifle. Any caliber/action style you like, provided its deer capable. Elk capable is nice, but only if you live where the elk do.
Battle rifle. semi auto .308 preferred, but anything from an M1 Garand to a .303 British (or other milsurp) will do in a pinch.
Heavy rifle. Your choice, but something bigger than a .308, either in bullet mass, or case volume. Magnums in 7mm and up, or big bores like .45-70. Your individual area plays a role in which would suit you better.
Now, we are up to 6, and the Mini 14 could be on the list.
Beyond these basics, you can consider a pistol caliber carbine, to compliment one (or more) of your handguns. And you still have 3 options to come up with before hitting your self imposed limit of 10. Maybe a brush gun? or something else?
Obivously, there is a lot of overlap possible, dpepending on your specific choices. I have way more than 20 rifles, currently, and do have a mini-14. I also don't have an AR, or an AK. Personal preference. My Mini14 does everything I need a .223 to do. I have other (and better) rifles for other things.
In my neck of the woods, used Mini14s still run cheaper than used ARs, although, there are some folks who are selling ARs cheap, cause they need the cash more than the rifle. For cost alone, I choose the Mini. I don't need match accuracy from a .223, I have other guns for that. What I want from a .223 is magazine capacity, light recoil, reliability, and reasonable accuracy, because in a SHTF situation, I'm probably going to be handing the .223 to a trusted friend/relative, while I carry something else. Like my M1A.
All else being equal (and it almost never is) bigger bullets tend to work better.