Bergara B-14 HMR or wilderness ridge 300 win are awesome guns, the HMR is a little heavy for a mountain gun but it does shoot great! both are right around that $1k mark
I am also a fan of the Bergara B-14 and the Tikka rifle. IMO for the price you will be happy with either one of these rifles as they both shoot tight groups. The only problem with the Tikka would be if you wanted to shoot heavy loads as it does have a slower twist rate, however a 190 has done well for the Tikka’s I have shot and owned.
.300 win mag. Stay away from Tikka. Tikka is a great gun, well made and most I’ve seen are very accurate but.... they only have a 3.340” mag box. So I guess if you run factory ammo you’ll be fine but I handload and my buddy bought a tikka and the short mag box has been a real pain. I have a browning x bolt and it has a 3.600” mag box which is nice for shooting long heavy bullets.
I have a Browning Xbolt in 30-06 that I have been really happy with and just ordered another Xbolt but in 300 Win Mag. Like the stock a lot for my LOP and the textured grip it has. The mag and the bolt seems to be quicker and smoother, better then my Savage 300 WM. My Savage is very accurate but do not like the bolt action as much and the mag does not go in as easily. There is a small "U" shape piece on the front of the mag that clips the unit in place which I have had snap before.