My.308 build used a DGW upper and a PSA P-TAC lower. Upper and lower do not have to be a "matched set" from the same manufacturer but going that route will pretty much guarantee correct fit and matching exterior contours.
Even being "DPMS compatible" does not guarantee that certain parts will fit. While PSA claims that their lower is DPMS Compatible, it is not.
1. The takedown & pivot pins are unique to the P-TAC lower. DPMS parts are too short and have different detent slots.
2. Same for the bolt catch. While all .308 catches are longer horizontally than a 5.56 gun, the P-TAC one has a unique tang for the mag follower to contact with.
For the most part, all the fire control parts are interchangeable with standard AR-15 parts. Buffers and buffer springs are unique to the .308 due to more recoil impulse. Charging handles for the .308 appear similar but are much longer to accommodate the longer upper receiver.
Another suggestion....use an adjustable gas block so you can fine tune your build to be fully compatible with whatever ammo you choose to use.
Most of your pre-existing 5.56 tools won't work with the .308. The receivers are much larger, so vice blocks won't fit. The spacing between the pivot and takedown pins is larger so holding fixtures won't fit. All the carrier assembly components are larger so some bolt tools won't accept the .308 bolt. The barrel extension and lugs are different than a 5.56 gun so things like reaction rods and extension wrenches won't fit. Barrel nuts are larger and not common to 5.56 guns. Accordingly, barrel nut wrenches may differ.
Obviously, pin punches and basic hands tools remain common for both platforms.
Building a .308 can be challenging if you mix up too many manufacturers parts.
Here are the results.....