>>1720362$1k for the rifle itself or is that budget for the rifle and scope combined? The most versatile and user friendly format for a hunting rifle is bolt action with a scope on top so long as it’s still balanced and light enough for off hand shooting. Other actions are fun and arguably better in short range situations but either can’t handle the chamber pressures of flat shooting cartridges or are out of your budget if they can.
If $1k is your rifle budget you can get a Tikka T3x and not feel like you’ve made many compromises. If that budget has to include the scope too then you may need to step down to something not as nice for the rifle like a Ruger American.
As far as scopes, a fixed 4x like the Leupold fxII 4x33mm is the best bang for buck for most hunters who are honest about their shooting abilities. If you’re budget conscious and not trying to shoot past 250yds or so on game stop here and go get a 4x. Don’t cheap out on the scope quality. Cheap out on the rifle and scope features first if you have to because bad glass will frustrate you so much more than the downsides of a mediocre rifle, and fancy features cheaply implemented on a scope are worse than a good but simple scope.
If you practice more than most hunters and want the versatility at range, variable optics in the 2-6 and 3-9 ranges are good. Manufacturers worth your time include Leupold, Nikon, Zeiss, Nightforce and Swarovski. If you get a variable optic you should plan on it costing roughly what you paid for your gun if not more.
Get good scope rings and be anal about proper mounting of the scope. You want to be able to rest your cheek on the stock and completely relax while looking through the center of the scope. If you can’t then you may need to use something to adjust the dimensions of your stock. Seems nit picky but nobody dies it and everyone would be more accurate if they did.