WHICH ONE .. would you prefer for target range shooting and just generally sending some down range plus occasionally hunting with
Realistically, unless you plan on suppressing it, 300blk is not really a viable option. The rounds cost almost double what 5.56 does, and the ballistic coefficient isn't as good either. 300blk is really best at being shot suppressed at 200 yards or less. 5.56 is still the best "general purpose" round out there and its cheap and very readily available.
I hope this info helps.
The last category you had pretty much seals the deal. At least in Arkansas. For plinking the 5.56 will be less expensive but, a 300blk will be the better hunting round. However, a compromise can be had. Get a good quality lower and a 5.56 upper and a 300blk upper for it. Midway USA, Brownell's, Mid South, Natchez and many others sell whole uppers you can change out. Doublestar, Black Rain Ordnance and lots of manufacturers sell uppers. Then you've got it made in the shade.
@paine-revere-1776 That's very true! I actually have a very similar situation where I have an 11.5 suppressed as my battle rifle with a mk12 upper as my DMR setup.