I had an early Rem 700 PSP in 308, that liked 173 to 190 grain Match ammo it was about a 1/4 MOA. My oldest son has a 1990's PSP that likes 168 to 175 Federal Match, he bought it off the Ohio Highway Patrol when they reduced Rapid Response Teams to just one.
After I bought a Savage 10 BAS and got the scope zeroed, I was shooting 20 shot groups that started .0 and sometimes .00. I sold the Remington as soon as someone would cough up 2 grand! (I traded for a Shiloh Sharpe's 1874 in 45-70 with lots of bells and whistles!) After my good experience with the 10 BAS I found a 110 BA in 338 Lapua. (That took 8 months) I shoot only hand loads to keep costs down to less than $4 a round with Virgin brass and about $2 for reloads. At 94 grains of H-1000 or 104 grains of US869 and 300 grain Matchkings, I get 2800 & 2900 fps respectively and 1/4 & 1/2 MOA at 200 to 1000 yards (respectively)
The aluminum chaises BA series has been discontinued for the BA Stealth & BA Stealth Evolution series But these MSRP at what mine did 12 to 15 years ago
There are better and much more expensive rifles, but why bother!
The only way you can find quality 308 ammo currently is through a SWAT team, buy older match ammo at a gun show, or load your own. My 308 BAS really likes Hornady 168 A-Max TAP Precision (LE only Ammo) I put 500 away for a rainy day and load Sierra 155 Palma Matchkings at 2900 fps and get less than 1/2 MOA on a bad day and almost zero MOA on good days! I use Lapua Match brass after the Hornady Match brass wore out! There is a big difference in the two; Lapua is worth the extra $$$!
On 338 ammo, there is no such thing a inexpensive! however There is junk! I bought 4 boxes of "Bitterroot Arsenal" That had PPU headstamp and 300 gr Sierra Matchkings. It shot no better tan 4 MOA at 100yards! (Sometimes some friends were getting 6 MOA) That is horrible in anyone's book!
I highly recommend Redding's Bushing Competition die set (now around $410; they were about $280 when I bought mine. The 308 set is now $360) plus you'll need a good shell holder and bushings. But what a difference they make!
Scopes, don't spend all that money on a rifle and ammo only to waste the capabilities with an "Affordable" scope! and spend the extra cash for the 56mm objective lens over the 50mm, there is 17% more glass to gather light on those far shots! Especially if your targets are in the shadows!!!
Since 338 Lapua was a "new to me" cartridge, I bought everything within 8-10 weeks. That was 12 years ago and ran $5700. I bought the best I could afford (or a little more that I could afford!) and all these years later I still have not had to upgrade a single thing!
Ivan