I know what the law is just what is the smallest round you would recommend I sure as heck wouldn't recommend a .243
You need to realize, what I’d use myself might be very different than what I’d recommend to the masses. Most shooters don’t show much dicipline when there’s a big bull across a canyon, and they have a valid tag in their pocket.
For them, the 30-06 would be a likely minimum. A .270 or 25-06 would also work, but a 30-06 would work better IMO.
For myself, I’d feel comfortable with a .243 Win. I know it’s capabilities, and I know my capabilities with it.
Even so, I’d probably opt for a 7mm rem mag or some such. It offers more options when it come sto taking a shot.
But, as a minimum that I’d use myself, the .243 could get me by.
I’m seldom a minimalist when it comes to bigger animals, but since that was the question, that’s my answer.
Daryl