Wood is easier to work with in case the lock up isn't as tight as desired. Shimming behind the forearm spacer works very well in this. The O-ring works, but often you might have to sand down the barrel channel inside the forearm to make sure nothing touches. No big deal, it only takes a min or 2.
Still some shoot very good with the synthetic stocks. My 243 barrel-standard contour- is great with just factory fodder. The Federal Power Shocks 100gr shoot always at 1" or under, mostly under at about 3/4. And it carries a synthetic forearm.
The main thing to look for is lock up and side to side play. If there are any then accuracy will suffer.
It's been said before by several and myself included, I like my Handi barrels to lower slowly when I break the action. Not just fall down. I like a tight fit.
Best bet is to buy the wood version and then later down the road buy a synthetic forearm to see how it fits your barrel to receiver. If it's tight then go ahead and pick up a stynthetic buttstock.
The 243's can be real shooters and a ton of fun too. I am working up a handload for mine now and this lowly standard barrel is really shinning. You might want to consider a 25-06. Lots of versitility and grain of bullet to work with.
-Aaron