I am not considering a 22LR or a .223 as I already have a .243
So do I, but that is not the issue.
I have to admit that I have been saving my 243 and not shooting it as often as I would like, mostly due to the fact that the rifle ranges available to me within reasonable traveling distance are 100 yard ranges. (and that is still a 45 min drive) There are some 300 yard ranges available but are a hour and a half drive in each direction and at that point gas is costing me more than ammo to do it often. Anything that is 600 meters or better is a 3 hour drive away, and that is what I would like to shoot at, but I very, very seldom have the time or resources to follow up on going there.
Yes, 308 would be better to practice with and barrel life a bit better but I would rather reload my own ammo than use commercial or mil surplus for better accuracy.
So I went with a bolt action 223 Remington (recent purchase) which is what I reload the most and cheaply, not because it is a better caliber (it is not) but because it gives me the most trigger time to practice the basics and hone my skills. Most skills are transferable for me and it does give me more trigger time.
Your circumstances may be different, if not you may want to try the 223 option, you can always use it for varmint shooting as well.
Brian has given you some very good advice and I would follow it, but things are never the same for all of us and you need to follow your needs.
Good luck and shoot straight.
Jim