If buying a new production rifle Winchester is at the top of my list with Ruger Hawkeye a close #2. $900 will just barely get you into Winchester. It will buy you a Ruger and a scope. If you can afford a bit over $1,000 Kimber is another good option.
Tikka makes a very accurate, but non-traditional rifle, priced at around $600. If you like the modern non-traditional look and features it is a very accurate rifle. Also the lightest rifle you will buy for under $1,000 if that is something you like.
Weatherby makes a good rifle. They are the heaviest rifles made though, almost 2 lbs heavier than the Tikka and about a pound heavier than most of the competition. If you want a heavy recoiling caliber the weight can be a good thing to manage recoil. I wouldn't be interested in one in a standard caliber.
Savage also makes a very accurate gun. They have some features I'm not crazy about but that is more personal preference. If you like them you will get an accurate rifle.
There is nothing Remington makes that I'm the least bit interested in. Quality concerns are probably over stated. There have been some issues, but most are just fine. I just don't like the guns design and feel there are much better options.