the cz's are top notch. almost all of them seem to be !!!! accurate. you also get a pretty sophisticated set trigger.
down here in australia, .308 is a pretty versatile calibre for competition. it is a sensible choice for field rifle sihouette, where 1000 ft/lb minimum is needed for the 500 yard targets. you can enter "f'-class 600 and 300 yard 3-position target matches ( calibres must be military - 223 or 308). of course, you can also play in field rifle benchrest.
the varmint weight of the cz might also take the edge off the 308 recoil, making for a more enjoyable day when sitting behind it at the bench. ( even the standard cz 550 is a relatively hefty 8lb bare weight. i'm looking at one in 308 for similar uses to yourself, freakingout).
if you handload, you can get 110-grain varmint projectiles, too, for a day plugging rabbits ( or woodchucks, prairie dogs or whatever you guys go after).
if you get one, let us know how it shoots