Ruger American is good for what it is - a good product among its class, which is "budget friendly" rifles. The 783 and Patriot are also in this class. I've handled a few of the Mossberg rifles, nothing pretty about them, like anything in their class, but each one I have handled has been a sub-MOA rifle, one of which was a half minute rifle with factory loads - which WAS in 243win.
The Rem 700, for all intents and purposes, is the Gold Standard by which all other bolt actions are measured. There are many flavors of 700's out there, but they generally share common traits for accuracy and reliability. A guy might comment the 700 is uninteresting, since they're everywhere, but they're everywhere because they're good rifles.
Personally, I would save up a little and get a 700 of a little higher grade, OR, I'd buy a lower end 700 model and plan on some aftermarket upgrades. If you don't mind a blind magazine, a 700 ADL can be bought for about $400, restocked for $100-150, bedded and trigger adjusted for about $100... Get about $600-700 into a 700 and you'll get a rifle together which will make you very happy.