You can buy 6.8 ammo for $9.99 /20.
If you don't reload, sell the brass. It goes for .30¢ each. That brings your cost down to $3.99/20. You can't hardly buy 5.56 for that. It offers a lot more power than either the 5.56 or the .300 or the 7.62x39 from a 16" barrel, and a flatter trajectory.
if you buy higher end ammo or reload, a 110gr projectile in spec II is about 2700fps. That same weight is 2375 in the BLK, and the heavy 5.56 is usually 2700-2750 from a 16"
right now is a good time to be in the 6.8 especially if you can't SBR or suppress the gun.
SBR I still say 6.8, but with a suppressor either alone or in combination with an SBR , the BLK is damn hard to beat.
You situation though, looks like the 6.8 is the best fit.
As for the 7.62x39, the BLK beats it in an AR all day long, with similar trajectory, but the BLK has better available bullets with higher BC that will make a difference past 250-300 yards, and the bullets expand way down extending the effectiveness. It will be more accurate as well.
The 7.62x40 has drawbacks. Only one maybe two ammo companies.
I like the Wolverine, but it's still not common enough for me, 6.8 (.270 bullets in a 5.56 case ), very good round though. This is an up and coming round , and it's gaining a ton of support. It just got started by a member here a year and a half ago or so, and it gets really close to the old SAAMI spec 6.8 velocities. It's one to watch, and I will recommend it if you hand load or if you don't shoot a ton of ammo due to supply. I will promise you though, this round will be offered by more and more companies soon. MDWS is where you want to go for this one. He's a member here and on 68forums, and a great guy.
The only real competitor is the Grendel, and it's really a wash performance wise between the two. The G has really upped it's shorter barrel game to just about match the 6.8 spec II, and the 6.8 Spec II can just about match the G past 1000 yards. The 6.8 though has more ammo choices.
I would recommend ARP for your barrel and bolt in 6.8, or really, pretty much anything they offer. I have two barrels from him, and they are both sub moa accurate, and I don't know anyone that doesn't get that much out of them. Ironworks Tactical is the best place for a complete upper. Bret is a mil vet, and will take care of you 100%.
Someone else can point you to the Grendel specialists if you go that way.
If I can help you with any questions, feel free to IM me, also go to 68forums and read up there on what is going pon with it, current info. I would advise that you go to each caliber's specific forum for up to date info, and look at what actual shooters are doing rather than just what you read and manufacturer's advertising data.