I have a 4x16x50 B&L 4000 (now Bushnell 4200) on my 22-250 and a 6.5x20x44 VX-III on my AR. I used to lean towards lower end of the power range. After shooting the AR with the stronger optics, that's the way I'm starting to go. You can only shoot as well as you can see.
If you can find one, there's a line called Intensity. Yeah, I'd never heard of it either. They are made by Weaver and were designed to go against the VX-III's. The economy collapsed and Weaver scrapped the idea of the intro of a new line. I bought one in 6.5x20x44 for my .204 CZ. Checked it side by side against the VX-III and it's about the same for WAY less $$$.
Primos has an equivalent to the Nikon Monarch that is evidently a lot for the money. I'd go minimum of 16 on top end, and 20x is not too much IMO. That said, cheap scopes can get very cloudy at the higher settings. I had a 6x18x50 Bushnell Banner on the .204 and took it off for that reason.
edit to add...target turrets are really nice, and be sure to get AO (adjustable objective) to eliminate parallax (very important.