With a 1:10-twist 28-inch barrel, you can shoot perfectly well to 1,000 if you load cannily. 'cannily' means selecting the right bullet for starters and avoiding some like the plague. The old 168 and 180gn Sierra MKs, and nearly all (Berger apart) older 168 thirties from Hornady, Nosler, Speer etc are dynamically unstable at 308 MVs beyond 800 yards and should be avoided. There are also many excellent bullets which are stable into transsonic terminal velocities (a curse of 308 at extended distances), but whose BCs are such that they are now ballistically inferior to more recent designs developed with FTR competition in mind. One such example is the 175gn SMK, an excellent and stable performer but whose BC is frankly poor by current state of the art 308 long-range bullet standards. In a 28-inch barrel, it will shoot OK to 1,000, but is far more wind affected than say more recent models from Berger, the Sierra TMKs etc. It will also be travelling at transsonic zone speeds at 1,000, while you want terminal velocities (>1.2 MACH / 1,351 fps) that exceed this.
There are lots of ways of skinning this cat - best of the 155s driven fast, top of the range mid-weights such as the 185gn Berger Juggernaut 300 fps slower, or 200gn and heavier bullets at around 2,550/600 fps. There are many ways of achieving the required MVs. I don't want to start reinventing the wheel in this thread as there are scores (hundreds?) of threads on this forum offering exceptional advice and sharing thousands of hours of actual experience in choosing load combinations for long-range 308 and producing handloads that work very well at 800 yards and beyond. Your rifling pitch rate lets you use nearly (but not quite all) heavy / long high-BC bullets in the 200gn and up range. The other factor is how is your rifle throated? Most of the super-BC bullets need significant freebores to allow long COALs and avoid over-deep bullet seating in the case. If short, you're better sticking to the best of the 155s or lighter bullets - the Berger 155.5gn Fullbore and 168gn Hybrid being two such. (Although the norm now in high-level long-range FTR is low drag 200s such as the Berger 200.20X and the new Sierra 195gn TMK / 200gn MK etc, I personally prefer and use this pair of lighter bullets in my custom-built FTR rifle.)
All I'll add is that if you are half-serious, start by buying one of the top quality small primer / small flash-hole 308 cases. They not only provide reduced MV ES values, but are very strong and accept high pressures for many loadings to get the last essential 100 fps MV. Until recently that meant Lapua 'Palma', but there are competitors now from Peterson Cartridge and others. Also, if you get into this, I'd advise buying Bryan Litz's book
Applied Ballistics for Long Range Shooting 3rd edition and studying it carefully. It provides invaluable information of bullet efficiency and stability and advice on choosing long-range bullets.
https://store.appliedballisticsllc.com/Applied_Ballistics_For_Long_Range_Shooting_3rd_p/0006.htm