You didn't say if you were hunting with it or target shooting.
Being fairly new to the AR scene and no longer much interest in shooting long range, it's more challenging to me to get the game close than shoot it way out there.
Unless you have a need for a fast second , third or more shots I'd back away from the AR in a custom or wildcat chambering. I have one in 20 Practical and it isn't fun to lose or dig out of the dirt brass that is expensive to buy or put effort into create.
A bolt action Rem or Sav. will be half the price, usually have a better trigger or reasonably priced replacement, less finicky to load for, manage brass better and a number of other advantages, So unless you need rapid fire I'd go with a bolt action.
Last year I built a nice little rifle from scratch for under $600. that I won my AR with. While the AR is very accurate, it is heavy and awkward to carry, it has a very crisp trigger but very heavy compared to my bolt guns. I'll most likely only take it out hunting just enough to say I killed a coyote with it, it will be a target gun for fun(serious target shooting will get the bolt gun) and maybe some work on PD's or GS's.
As far as cartridges I doubt that there is a whole lot of difference in accuracy from 243 to 308 with the premium target bullets available today. For many years the 308 was king on the MS coarse but the 7mm-08 made inroads due to flatter trajectory, less recoil and still be able to knock down targets. That was in the 1980's I haven't followed any of the LR sports since then.
Have fun with this, putting together a rig is as much fun as shooting it.