For anyone researching this topic, I would skimp anywhere possible and put ALL possible money into the barrel for your first precision build. Cheap bolt carrier, standard charging handle, cheap lower parts kit, etc.
The key to barrel price is NOT going fluted. Fluting makes hitting your weight goal easy but is very expensive costing almost half your current barrel budget on a custom barrel. I would not get a Criterion, personally, too hit or miss in my experience. I would look at a CLE and WOA on sale but ask them specifically about their 16" SPR profile weights. Some exceed 32oz. slightly. That Ranier 16" may be over 32oz. as well.
Also, be prepared to try lots of different factory loads to see what your barrel likes and be prepared to buy 1000+ rounds of the EXACT lot of ammo you find your barrel likes, not just make/model/weight but the actual LOT. Ammo is AS important as the barrel when it comes to accuracy and if you find a .5 MOA loading you need to buy it in bulk because seating depth, powder, primer seating/sealing, etc. frequently change in factory ammo. You can tune any handload via seating depth, but factory ammo is what it is and the "same" ammo is only the same in a given lot.