Well I think I would be more in line with Art's comments, but I think it all boils down to the terrain, and other conditions you hunt. For me, the minimum would be something on the order of a 7x57, or maybe a .308 Win. For years I hunted in northwestern california. I used an 18 inch barreled springfield 1903 and 180 gr round nosed bullets. A big brass front sight and a wide open peep. I sighted in at 100 yards. Where I hunted, 25 yards was a long shot. A .243 would have been totally useless there. Later on, I inherited a 6.5 Mannlicher-Schonnauer from a friend who passed on. The 160 gr. bullets were perfect for my hunting situation. Some lowlife stole that rifle. I now use a Ruger International in .308 Win. for most of my deer hunting. My wife liked mine so well, that I had to buy her one. Same caliber.
My thoughts on the .243 for deer? Well. If you are an experiences hunter who is willing to either pass up dicey shots, or can wait for the proper opening to shoot, then I would say OK. If you are the kind who gets excited and cannot wait for a shot, then get something with more clout.
I just flamed a guy in another forum because he was bragging about using a .243 with the 85 gr. Sierra hollow point on elk. On elk! He was flaming me because I prefer heavier bullets that pass on through leaving two holes in my game. Oh well. To each his own.