Sure thing, since your uses will be hunting and targets to around 500y, and your budget is right around $2200 for the rifle, this is what I would recommend:
Upper
- Barrel: Falkor DRACOS:
https://www.dracosbarrels.com/produc...arrel-18-inch/ 18in $850. Comes with adjustable gas block and tube. If you want a different caliber (more on that below the build) they make them. The 18in is a good compromise length for your uses. If you'd rather go with a more traditional barrel have CLE spin you up a bartlein blank for ~$450, pair that with a Superlative Arms or SLR Rifleworks gas block.
- Upper & Handgaurd: Aero M5E1 kit:
http://www.schuylerarmsco.com/produc...d-black-96-993 $350.
- Bolt Carrier Group: Aero Phosphate $190
http://www.badgerstateordnance.com/p...errations.html
- Charging Handle: Griffin Armament AR10 SNACH:
https://www.rainierarms.com/griffin-...arging-handle/) $81.
- Muzzle Device: A suppressor. Use a cheap $6 .30cal A2 while you wait on the paperwork. If you'd like suppressor recommendations, let me know.
Lower
- Lower Receiver: Comes with kit.
- Small Parts: Any triggerless ar15 (yes ar15) LPK $25 (redbarnarmory has free shipping).
- Trigger: ELF AR10 trigger:
https://www.redbarnarmory.com/Elftma...t-p/elf308.htm $250.
- Buffer Tube/Weight/Spring/Stock: M5 Carbine Kit
http://www.schuylerarmsco.com/produc...stock-57-993 + Luth-AR Carbine stock ~ $220. Feel free to swap the spring to a Tubbs AR10 and/or remove the weights from the buffer.
- Grip: Tactical Link PDW or BCM or Magpul or B5, ~$21.
Accessories/Misc
- Bipod: Bipod & Attachment: Impact Weapon Components Mount-N-Slot V2 $26 + Harris 9-13in swivel $100.
- Sling: BFG Vicker's $59.
- Magazines: Lancers for factory ammo, Larue/KAC if you are going to reload.
- Lube: Slip 2000 EWL.
If you want to change it up, raise/lower the budget, discuss parts, need guides, or just have general questions let me know.
Ok, now onto calibers. A .308 is great but I just wanted to let you know there are other good options.
1.) .308/7.62x51 will have the cheapest plinking ammo out there if you don't reload. It will also be the most locally available (if that matters to you, I order everything in bulk). However the cheap ammo will not be accurate, so it is really only good for speed drills and blasting away at steel, precision work will require match ammo, which is just as expensive as 6.5 Creedmoor or 6mm Creedmoor match ammo.
2.) No matter which caliber you decide on, you should probably reload if you don't already, at least down the road. Better accuracy can be attained than with factory ammo, and at considerably less $/r. It also opens up calibers with better ballistics.
3.) Any caliber from an AR10 will kill deer (highly recommended) and kill paper at 600y+. The 6.5 Creedmoor, 6mm Creedmoor, 7mm Creedmoor, and others will just do it easier, with less drop and drift, and more energy on target, and it is much easier to track your shots due to lower recoil. Whether that is worth the increased cost per round for plinking ammo and/or having to reload sooner rather than later is up to you. For me I'd say go 7mm or 6mm Creedmoor. Here are some resources that should help: All pros use 6mm or 6.5mm for PRS
http://precisionrifleblog.com/2017/0...-the-pros-use/, and going to 6.5 Creedmoor increases probability to hit 700y targets by ~25%
http://precisionrifleblog.com/2015/0...tridge-matter/ due to less drift (which is insane).