Re: Advice on which .243/6mm
Do some research into the 6BR Norma, I think you will be impressed. Many 1000yd BR shooters are now using this and 105/107gr bullets. From 30" barrels, performance is very good, brass and throat life is wonderful, recoil is very mild. Ensure that you are using the long throat version.
If not, I would go with the 243, Reg or AI is up to you, because cases are so easy to get and you can form from 308match brass if necessary.