With your caliber restrictions the best ones I can recommend would be the P14 or M1917 Both will suit your needs, nice aperture sights, tend to be fairly reasonably priced and as long as the bore is in good condition will shoot very well.
Others I would possibly consider if you chose to broaden your caliber restrictions would be a Swedish Mauser of M96 or M38 variety, a Swiss rifle of any sort (most immediately say K31 but the other rifle variants like the G1911 or G96/11 will shoot just as well for less), or any Mosin Nagant with a great bore.
I haven’t had a Mosin Nagant which shot poorly yet and I have had over a dozen of a few different models, mainly Soviet variants (M91 infantry, M91 dragoon, M91/30s, M38, M44). Usually the limitation with them is the cheap surplus ammo, not the rifle itself. Once fed good quality ammo the groups tighten right up.