For budget night vision, the Sightmark Wraith is hard to beat. I have the 4-32x50 HD with a Sniper Hog Lights 66LRX illuminator on my Savage Axis 243. Haven't had it out for actual hunting yet, but played around with it. With what I have, I have no problem seeing out to 400 yards and probably farther if you really wanted to. That's not guesswork FWIW, that's known distances confirmed with a rangefinder. Because the zoom is digital, I wouldn't expect to zoom in farther than 16x and expect it to be usable as far as pixelation. You could get the 4K version which is 3-24x50, more expensive but still under budget and better resolution.
Also, aside from being a night vision scope, it can also be used during daylight too which is nice.
SHL makes one size larger light (the Coyote Cannon) which can reach out even farther but is twice the weight and 400 yards is farther than I'll ever shoot. They also make smaller illuminators that are still upgrades over the stock Sightmark one as far as brightness and throw. With that being said, under 200 yards you MIGHT be able to get away with the stock illuminator, I didn't experiment enough with it to really get a feel as I bought the SHL illuminator right away.
My whole setup (not counting the rifle and stock) cost me:
$375 for the Wraith (law enforcement discount direct through Sightmark)
$165 for the illuminator/mount/batteries/etc. (Not shown in my picture below, that's the stock one)
$60 for the bolt action mount for the Wraith through Ron Bimmer Outdoors. On a bolt action, you'll want this to move the scope back for proper eye relief. If you run it on an AR, you shouldn't need it.
So, about $600 for the whole setup.