Welcome aboard- glad to have you amongst us.
You can get quite a few options on varmint rifles, plus scope, plus a fat supply of ammo for your $1k mark.
Before I just jump in and start naming makes and models- I guess it's fair to let you know there are a few things to consider. If you're going to be carrying the rifle for very long or very far- you'll want to steer towards the lighter end of them. If you're ranch shooting from a bench/truck- then it's OK to go with the heaviest out there.
How much shooting? If you're going to be on frequent heavily populated p-dog towns- then you might not want a barrel burner. If you plan on yotes and occasional other critters- then your high-speed rounds aren't a bad way to go.
For one that will hold it's own for just about anything from yote on down, and medium weight- then the options available might make your head spin. If this looks like your goal- then I have to pitch my vote for either the CZ 527 American or the CZ 527 Varmint either/both in .223 flavor. Now if you want to step it up a notch, then the AR's are the way to go- but that will end up over your budget by the time you get some decent glass mounted.
For glass, I absolutely see no reason at all to spend as much for the scope as you do for the rifle. I have several Mueller 8.5-25x scopes that have held up every bit as well as my Weavers and Leupold.
If you can't get a clear deal on a CZ, then take a look at Savage, Remington, or the Howa lines. I'm not real familiar with their models. If you do consider the CZ, aside from their accuracy and overall quality- they have a single-set trigger. The regular pulls are OK at hunting pull weights, but if you thumb the trigger forward and set it- it becomes a matter of a pound or less. It'll really let you get the full useful range out of the .223 round.
Hope that helps a bit.