I have owned the ATN 4K PRO 3-14x and now the 5-20x. I'd skip the Buckhunter unless you just plan on using it in daytime only. The PRO gives you day and night use via included IR light. Scope rings are included.
I'd recommend the 5-20x for any shooting past 30 yards because the "zoom" on these scopes is digital, not optical. So the 3-14x scope has a 3x optical zoom and 14x digital zoom. The 5-20x scope has a 5x optical zoom and 20x digital zoom.
The 3-14x is good for those shooters hunting hogs and coyotes where they need to scan a large area quickly. I found the 3-14x to be subpar for any sort of accurate shooting past 30 yards when it comes to airguns and the small holes they create on paper because I had to always zoom in up to the max to get any sort of good accuracy, and the image quality wasn't that great at full zoom.
The 5-20x is more suitable for airgun work because it's already zoomed in more and even at 20x it gives you a slight advantage when trying to shoot accurate groups.
That being said, I tried to shoot at a large white steel gong (12" metal gong) at 60 yards with my 25 cal Crown, fully zoomed in, and it was very hard to see the groups I was printing at that distance.
That being said, these scopes are good for larger calibers where trajectories are flat using powder burners and precision shooting is less of a requirement.