Given the listed requirements, make sure it's a good hunting caliber first. If plinking paper, then relatively inexpensive.
The problem right there is whether 5.56 is 1) legal to hunt with in your jurisdiction, 2) adequate for the game. Then you have to decide what proportion to ammo cost to allocate. I built a 6.8 because I wanted 40% more power, and hunting uses a lot less ammo than target shooting. To get cheaper ammo, I'm planning on buying a reloading press next tax entitlement season, to reduce costs about 50%.
Another decision is whether it's an AR15 or AR10. .308 is a major step up in power, ammo is cheaper, the weapon is two pounds heavier. It's possible to get one used under $1000, but not likely new at all.
Since it's this world, prioritize your needs. One or two of the ideal requirements are just going to get left behind, like it or not.
What will you do with it 85% of the time? If it's paper, 5.56 will get the job done. Long distance is possible - but accuracy out to 600m means it won't be a carbine, more likely a varmint/precision rifle. That makes it a tube free float, fixed stock, A3 upper, lo pro gas block, with scope and bipod. A good name brand stainless precision barrel is mandatory, and you should buy with that requirement up front.
If it's hunting first, and plinking for fun, then maybe a carbine will do. Effective ranges when hunting are less than 300m, simply beccause most game animals are hard to see beyond that in their environment. Prairie dogs, woodchucks, and antelope aren't the normal game most Americans hunt. It's whitetail deer, and they live in woodland edges with limited visibility. That also means the large scope of long distance shooting is a disadvantage, a red dot does the job much better. For picking up on a close target that will only be visible for seconds, red dots get the job done. So much so, they are the primary optic on the M4 now.
Decisions, decisions, the first one counts the most: What range, what target? Determine that, everything falls into place after as it contributes to the desired result. How? First, caliber/cartridge, then barrel, then optic, then furniture, then trigger. In that order, you can build a very specialized gun, or an all purpose one.
EX: Hunting rifle on whitetail out to 300m. I chose 6.8SPC - others bias their choice by what other things they might do. I got an ARP 16" midlength medium contour nitrided barrel, and A3 upper with rail for a red dot, fixed A1 stock, Tango Down Battlegrip, rifle length handguards, a FSB at the rifle position, an issue trigger with adjustable takeup screw, and linear compensator to move the maximum amount of noise forward.
A 600m gun would be more likely a 6.5Grendel, with stainless target barrel, perhaps a monolithic upper for 4x12 minimum scope, adjustable cheek weld stock, an Ergo grip, bipod, and no flash hider. It would also be nearly AWB compliant, if that's a local complication.
Narrow down what range, what target for 85% of what you want it to really do, and the rest should fall into place with no compromising. Then it will be fun and accurate, not a PITA and something to regret.
