If thats your budget I would go with something very easy to find upgrades for (savage or remmy). Your scope should cost as much or more than your rifle. You can do a lot of things to a cheap gun to make it shoot, the same connot be said about scopes.
I put together a pretty wicked coyote rifle for a total of $1150 CAD, including dies and mounts. It was in a .243, but you could easily find a 300win or 7rem mag for the same price.
Local sports store was selling Remington SPS's for $515 (up here thats a good price), so I picked on up. I tore the stock apart, and using steel and fiberglass, turned that cheap stock into a decent feeling thumbhole. I bedded it with JB weld (ok for smal stuff but use devcon or similar for any magnum), and opened the barrrel channel WAY up. Injection moulded stocks move a ton, so I made it so there was 3/16" gap on both sides of the channel. **This seems a little extreme, but when I was hunting yotes in -32*C there wasnt even 1/16" on the one side and a big gap on the other.**
From there I bought some leupold mounts, simply because I couldnt get anything else in my location. I buy Warne or Talley for budget stuff if I have the choice. I mounted a Vortex viper PST 2.5-10x44 to that and started load development.
Using 95grian bergers and 4350 I have been able to hold 1MOA or better to 800 yards depending on wind (maybe a bit more if its gusty
). I really like the PST's for an entry level scope, they have all the bells and whisles that a true LR tactical scope needs, you can even get them in FFP. And yes, 10x is great to 1K.
It is easy to upgrade from here with stocks, triggers, bolt knobs, muzzle breaks.... and it can all come in time once you have a good foundation. The first thing I would replace is the stock unless the trigger is brutal. laminates are very good for the money and most people can do the woodwork themselves.