how about another way of addressing this question....
Start with a Rem 783 in 308 (various Savage SA's will also work). Around $400 to 500'ish new... A new Shorty version with nicer features may be closer to the $500'ish range.
Plenty accurate and easy to set up for hunting. The rifle pictured is in 243 but the 308's shoot similarly. Great mag, trigger and function. Sub MOA capable. I added an EGW rail for $56
I detest the factory bolt knob so converted it to a aftermarket tactical style knob. $35 or less for the knob... some labour, or gunsmith... done. Cerakote and looks like new.
For the precision side of things, add a Boyds pro Varmint or MDT LSS chassis. The black PV is around $225 Cdn. MDT LSS is around $400 plus AR furniture, grip and mags.
Add a match grade prefit in any short action chambering (that fits your bolt head) .. I really like the 6.5 CM. Prefer a 6 Dasher.. or a hot rod 22cal like the 22 Creedmoor? Starting at $465 ($100 for muzzle threading). Easy to swap the barrel at home with gauges, barrel nut wrench and a strong vise (gauges are $36 each, wrench set $48).
Do some handloading and get some 1/4 to 1/3 min groups at 100yds
Some nice performance at 250yds.
Take it out to 1450yds
And shoot some rocks for S&Gs
Convert the rifle back to factory dress for hunting. The factory plastic stock is quite comfy for a hunting rig and has a great recoil pad. Pretty sure I haven't spent $1500 yet.
PT&G does make DBM if going conventional stock.. that adds a bit to the price tag depending on how much work you can do yourself... but you are still way under $2k.
There are now more rifles that can be converted in a similar way.. Savage Axis (not my fave but it can work), Savage 10/12 - Stevens 200, base Howas, Rem 700s (yep, even these)..... kind of sort of Tikka T3's
If a factory rifle doesn't float your boat, just build it...
YMMV...
Jerry