I immediately think of a Springfield 1903 but what are some other good options?
Which are the better ones?
IMO, the peep rear sight on the M1903
A3 is typically much better for competition that the earlier M1903 rear sight - at least for some middle aged guys who can no longer focus as well on the small rear notch of the original M1903 rear sight. I see some good shooters use that platform at CMP vintage matches. It has easily adjusted windage settings and you can buy a new Criterion barrel for them, which may outperform an old WWII era barrel. So that is one is a solid recommendation (see bottom rifle as an example and note placement of rear sight).
The M1917 with its 26" barrel is another good choice, but windage is not field adjustable on that rifle. I've seen some guys do well with these rifles, and one day I plan to use my Remington M1917 in a vintage bolt action match. (top rifle in the attached pic) Match ammo in 30-06 is easy to find.
Some serious competitors use the Swiss K-31 rifles, which have good accuracy potential even with surplus 7.5 Swiss ammo, but I think re-loading is probably advisable if one uses this platform a lot for competition. (not shown)
https://www.thetruthaboutguns.com/getting-started-cmp-competition/
As another member noted, the Swedish M/96 or shorter M/38 rifles are also accurate rifles, but the rear sights are not that great. (middle rifle) Match ammo is available in 6.5 Swede, but you have to hunt for it, as the supply of surplus M/41 ammo has pretty much dried up at this point.
So those are my suggestions. (I typically use my M1 Garand at CMP vintage rifle matches, and my M1903 w/ 8x scope for vintage sniper match)