I'll say that in my experience, none of the mass produced China made scopes being sold in the US are worth a dime. I have one Mueller that is ok, but not something I'd put on a rifle bigger than a rimfire and even then it would sit on a plinker. All of the other BSA, Barska, Simmons, Tasco, etc that are made in China have been a disappointment sooner than later. The older models made in Japan or even the Philippines can be decent, but the current options are very poorly made. I've bought them in hope of a true value, and again, sooner than later, they have all been a disappointment.
With your budget, I'd put $300-$500 towards a scope and the rest towards the rifle. You don't need to spend a ton of money to get a quality scope. Options from Leupold, Bushnell Elite, Burris, Sightron, Weaver, Nikon, Ziess, and the Vortex Viper line would all be quality options, most of which have a line or two that are reasonably priced. A good scope goes a long way. You spend your shooting time looking through it and if it doesn't work, it's nothing but a pain. Some of the cheaper scopes work for a little while, but they tend to fail much sooner than those listed right above.
I would be much less picky about the specific rifle I bought than the scope. Most rifle models today are well built. Some better than others and some are known to shoot better than others in general, but the bigger question for me is finding a quality scope.
In the $500-$1000 price range you can grab yourself one of many Remington, Savage, Winchester, T/C, Howa, Weatherby, Tikka, Browning, CZ, FN, Ruger, etc, all of which have their pros and cons, depending on exactly what you want to shoot and how you want to do it. In the 600-800 yard range, all of these companies make a quality rifle that will shoot well. Some do better for different types of shooting, and narrowing down the features of the rifle will narrow down models that fit your needs. Still, don't skimp on the scope if you have the money and buy a rifle from a known manufacturer and your more than likely going to have a combo that works well.