If you are going to be hiking somewhere (where?) in a SHTF scenario, then the weight of your rifle is the least of your worries.
Most of your weight will come from water, food, clothing, etc.
And if you think you are going to survive for long on your own, well, good luck with that. You need to sleep sometime.
Best bet is to form a group. Then you can spread out the load. Makes concerns about ammo weight less of an issue.
Really, ANY firearm in such a situation will serve you well. A .22 is a good idea, but lacks range and punch. If you are in a group, you can have a mix of arms to do different things.
I am always amused at the folks who think they need to stockpile a million rounds of ammo to survive. Really, you just need enough to stop the BG and then take his weapon and his ammo. So, a useful skill is knowing how to use and maintain various types of firearms. If you only know how to run an AK, you might want to learn how to run and maintain an AR, SKS, lever gun, and bolt gun.
Just some random thoughts.