Luky,
I'm going to be contrarian and recommend against getting a short barrel.
I've noticed that short barrels are now all the rage, with 16" barrels shooting to 1,000yards all the time...on the internet.
I shoot mostly across the course matches (200,300,600yards with iron sights) and prone matches, 300,600,1000yards, again with iron sights.
I shoot XTC with my AR-15 service rifle (20" barrel) and long range with my M110 build (also a 20" barrel). Short barrels are a stupid idea for long range.
If you intend to mostly shoot prone matches, or a building this rifle to shoot long distance, do not take the advise you've gotten so far.
There is a reason why F-class, palma matches, and NRA long range matches are shot w 28" -32" barrels...they produce the muzzle velocity needed to not only reliably get to 1,000yards, but do so while placing most of the shots within a 5"-10" circle with crosswinds.
To this end, I would go with the longest barrel i can get my hands on.
I have a 30" Brux barrel for my 308 AR platform...it cost me $480. I haven't been able to finish the build due to the madness afflicting the industry and because well, i'm busy shooting across the course and trying to keep enough reloading supplies on hand.
If this rifle will be exclusively a range queen, then go for the longest barrel you can find. I think you will find that even a 24" barrel is on the short side for this application (tho not too short). A 30" barrel will give you about 100-200ft/s over a 24" barrel which in turn translates to 200ft/s-300ft/s over the 20" barrel lengths you are being advised to go for.
Call Brux, Satern, Bartlein et al and find out who can give you the fastest turnaound.
P.S. 175SMKs are just OK for long range. There are MUCH better bullets hornady's 178 HPBT, 208AMAX & 225 HPBT sitting atop RL-17 are much better choices than the 175SMK. Berger 175s, 185, etc are also excellent bullets.