Two questions that must be asked...
1. What do you want to do with it, or what will be it's purpose?
2. Do you reload? And if you don't but have lots of money to burn pay no attention to this question.
First I will address it's purpose.
1. Long range (500 yards plus) = 6.5 Grendel
2. Longer range (100-450 yards) = .204
3. Mid range (100-400 yards) = 5.56, 5.45, 6.8 SPC
4. Shorter Range (100-300 yards) = 300 AAC/Blackout, 7.62x39
5. Short Range (50-150 yards) = .458 SOCOM, .50 Beowulf
These ranges listed above are what I would consider their optimal ranges, obviously you can shoot under, and have the potential of shooting over with greater holdovers and wind effect, etc.
Now the second question.
1. If you have plenty of money to burn disregard the following, and just pay the premium for these specialty rounds.
2. If you do reload then any of these can make sense on a budget, however some make more sense money wise. The 300 Blackout brass can be sourced from 5.56 brass. 7.62 and 5.45 brass will be easy to find to reload. .204, 6.8 SPC .458 SOCOM and .50 Beowulf, I don't really know but I imagine that the .204 would be the easiest brass to source.
3. If you don't reload and don't have money to burn then I would get one of the following: 5.56, 5.45, or 7.62. They are all military cartridges that can be bought for cheap, especially the 5.45.
The 7.62 however has had some problems in getting it to run right in the past, I don't know if they have been worked out, but for me I wouldn't even consider it being that I reload and there is the 300 AAC/Blackout.
Personally, the three I would consider for my personal preferences are the 5.56, 300 AAC/Blackout, and the 6.5 Grendel. The others that interest me are the .458 SOCOM and .50 Beowulf, that's about it for me.
If I were you and you reloaded I wouldn't hesitate to buy/assemble a 300 AAC/Blackout, it is easy to reload for and if you already shoot magnum handguns and reload the powder that is used crosses both platforms. The Blackout is seemingly picking up interest and I wouldn't be surprised to see a more ammo manufacturers ramping up production to meet demand which might allow for cheaper commercial ammo purchases.
P.S. Forgot to mention the pistol cartridges, but that can be more self-explanitory.