Link doesn't go to the stock, but in general yes you will need the stock, buffer tube, buffer and spring. The UBR parts will not work on the ARFX stock.
I have a 21, but if I did it again I would go with the 24. It is only for cosmetics so my longer mag tube would better match the barrel. Gotta make sure everything looks good ya know.
The PRS stock for the 308 will have a shorter cheek rest as to not inter-fear with the longer top charge handle on 308 type rifles that use top charging handles.
If you have something that doesn't have a top charge handle, it shouldn't make a difference if you use a 223 stock.