The heavy barrel versus light barrel accuracy debate will go on forever, I suppose.
GENERALLY, a quality lightweight barrel will shoot as well as a quality heavyweight barrel with everything else being equal.
The differences in grouping ability between a good heavy barrel and a mediocre light barrel are apparent to most shooters, and it's assumed that the weight of the barrels is the big difference. Not so! the reverse could just as easily be true, that is, a light weight barrel can outshoot a heavy barrel. Many other factors come into play (bedding, handloads, rate of fire, etc.)
Where a heavy barrel really shines is that it tends to REMAIN more accurate with long shot strings, such as in benchrest competition, or in any timed competive shooting event. It would have little bearing in most hunting situations, with the possible exception of target-rich varmit shooting.
Probably none of this would apply to your intended use for a single-shot .243 Winchester. I have a reed-thin octagon barrel on my .243 Win mauser action, and it shoots quite well, but only for SLOW FIRE shooting!
For your purposes, the .243 W is an excellent choice and with moderate recoil. With good handloads, it might really surprise you with it's basic accuracy too!
You might think about the advantages of a lighter weight barrel for ease of carrying, handling, etc. Don't let accuracy be a factor in deciding. Good luck with your new rifle!
