I'd recommend that you ask yourself what's the next step beyond the 200-300 yard game and 12in plates.
If you think the itch might need more scratching, and you'll want to challenge yourself with longer distances and smaller targets - 6.5CM is the way. It offers a ton of advantages in accuracy and good precision ammo availability (panics excluded) as well as somewhat reduced recoil. If you're going to push yourself and your skill as it grows, you'll get a lot more efficacy for a given skill level using 6.5CM. I will say that it is VERY satisfying to hit steel at 800+ yards and the only reason I don't already own a 6.5CM is because I've got so many other .308's.
If you think you're going to just love the 200-300 yard life and clanging the same steel over and over again, forever, or your situation/range availability precludes longer ranges or smaller/more interesting targets, then wider availability and generally lower cost of blaster-grade .308 (again, panics excluded) is worth considering instead.
Wildcard option - if you really want to build your marksmanship skills and learn how to read wind and play all those rifle marksmanship games, consider instead a Ruger Precision Rifle in .22LR, and learn to call wind at 150-200yd with that .22. It's fun, inexpensive, easily suppressed, and fun for literally anyone physically large enough to get a proper firing position behind it. It's also substantially less overall cost to 'get in to' than .308 or 6.5CM. Better still, you will NEVER have a problem selling a .22LR RPR and getting a good chunk of your money back for it, should you decide you don't like it.