I wouldn't mess with a Ruger American. They have mag and feeding issues. I've sent 2 up the road and have been dealing with Ruger with a third in 22-250 with feeding issues.
I like Tikka. I also Like Sauer 100's. I would rather have a Winchester Model 70 than either though but they can be hard to find in the caliber you want right now..
Weatherby Vanguard or Howa is also decent. Browning X-Bolts are good.
I would stay away from any of the entry level models like Savage Axis, Rem 783s, Browning AB3 or Winchester XBR. They feel like cheap junk. I would put Ruger American with them.
Most rifles are very accurate anymore because of modern machines. You'll just need to find somewhere to go look them over and hold them. See which you like best.
