It ain't the arrows, Tonto.
Unless you're a hand loader, I'd suggest that you start with .308 Win. You can pick up a Remington SPS Varmint with a 26" barrel (for roughly $550), drop it in a Bell & Carlson Medalist stock ($207-$407 from Stocky'sStocks) and have it skim-bedded and the barrel free-floated (my gunsmith charged me $100 to do that). Put a 20 MOA base rail on, put on medium 30 mm rings (all in, about $60) and get a Vortex Viper PST 6-24x50 scope (you can get them in MOA/MOA or MIL/MIL reticle/adjustment knobs and First Focal Plane, for about $900-$950). That's the set-up I started with (using a B&C A5 Medalist stock). The cheapest way to go is the M40 Medalist stock (I used the one that came on my Rem 700 5R with my Rem 700 SPS-V in .223) when I dropped my 5R action into an AIAX chassis with a NightForce 20 MOA rail and rings. That set-up was a little pricier (I recommend Mile High Shooting Accessories in Erie, CO...wonderful folks and DAV-run business...absolutely first-rate!). and a little more consistent than my SPS-V. NightForce Optics are a step up from Vortex Viper, but I may go Vortex Razor for my next scope).
For ammo, you can use Federal or Black hills Match as well as several other brands. 168gr bullets will work nicely out to 600+ yards. For longer distances you'll want to use either 175-178gr bullets or 190gr bullets.
BTW, since Remington has recalled almost all their X-Mark Pro triggers, you may want to get a Timney 510, with long sear (needed for the Varmint), or a Jewell replacement trigger. I replaced all my Rem triggers with Timneys (wonderful customer service from Timney, and either you or a qualified gunsmith can install them...they'll preset the pull weight to your request when you order from them). My initial rifle is a 1/2-3/4 MOA shooter to 300 yards and cost me $1,900 all in with the Timney recently added at $134. For $2,000+ it's a great starter that still shoots better than me (note the arrows remark, above).
I hand load so my match ammo costs me about $0.40/shot. I use ammo with 175gr Sierra Match Kings and Hornady 178gr A-MAXs and either Alliant Reloder 15, Norma 203B or IMR 4064 powder, depending on availability. I follow published min and max for working up loads.
Now most of the really good shooters use 6mm, 6.5mm or 7mm calibers for their higher ballistic coefficients and sectional densities...and I'll probably rebarrel one of my short action precision rifles with a 6.5mm. I have a hunting rifle in 6.5x55 SE, a wonderful caliber that has been widely and successfully used in 900 meter matches in Europe. The advantage of starting with .308 Win, however, is cost and gaining valuable learning and experience with reading wind. Zak Smith, one of the sport's leading players, has written some wonderful articles on getting into long-range precision shooting with well-tried and tested advice. Attached is the URL of the first, starting with equipment.
https://demigodllc.com/articles/practical-long-range-rifle-shooting-equipment/
I'm still a novice IMHO and will be for some time to come, though I have been a shooter for more than 60 years and a NRA certified instructor for some years. Read Zak's series and start shooting.
Good luck and best wishes,
FH
