Barret is not a better rifle than the Sako. The only thing Barret has going for it. Is that he refuses to sell to CA LEO agencies because CA banned his 50bmg rifles.
First off you are shooting 15 15 and 20 rounds in an F-class match or there abouts. That is fifty shots in a short amount of time. Can you handle the 338 Laupa mag recoil? Have you ever shot one.
Most F-class stuff is shot with 308 and smaller rounds. You the shooter gets fatigued as the day goes on. In my area we are on an open firing line in the HOT SUN for most of the day. Banging away with a 338 is not going to be conductive Long distance accuracy about 75 rounds in a day plus most people will not want to be within 50 feet of you shooting that monster with a break on it.Your not going to make any friends on the line with that monster either. F-TR is shot only with 308 win. Most use 175gr or 180gr Match bullets. Sierra makes a 155gr Palma Match bullet because in Palma shooting you are stuck by the rules with a 308win 155gr bullet. F-Open can be any caliber under 50bmg I think. At my F-class shoot it is all shot together.
For starting out in the F-Class or 1k bench rest. Look for the Savage F-TR rifle in 308 win. While the 308 is not the perfect 1k rifle for F-class it will let you get started for $1k + optics. the Sako is going to set you back at least $4k just for the rifle.
For me startign in the F-Class world I would get the following set up.
Savage F-TR in 308 win. Savage 12 F/TR 308 SHIPS FREE : Bolt Action at GunBroker.com
Badger Ord 20MOA rail. Badger Ordnance Maximized Picatinny
Leupold 30mm Mark 4 Picatinny Rings Leupold 30mm Mark 4 Picatinny-Style Rings Matte Medium - MidwayUSA
Sightron SIII 10-50x60mm Sightron 10-50x60 SIII 30mm Riflescope
If you don't reload I would also invest in 2 cases of Black hills 175gr match ammo. Black Hills Ammunition 308 Winchester 175 Grain Match
Total $2997 + Tax and fees.