For a varmint rifle, you'll (IMO) be best served by a relatively high-magnification variable, 14-32x on the top end. For an $800 budget, I think you'd be limited in FFP choices in the 4-14 and up range. FFP scopes tend to have coarser reticles in the middle of their adjustment range compared to SFP, as well. A fixed 10-12x may be a good alternative, as well, but would be a compromise for both PDs and coyotes. The savings may be worth it, though.
I would also discourage QD mounts, as PD shooting is a precision thing, and that typically means mounting the scope as solidly as possible, plus regardless of the ease of removing the scope and rings is offset by the need to re-zero in the other rifle(s).
I'd suggest a Weaver one-piece base and Burris Signature Zee rings (still "removable"), and a Vortex SFP Viper PST with as much magnification as you can afford. Of course, any competitors would be worth comparing, too.
As another alternative, a much cheaper scope like the Mueller APT may help you get your feet wet, and is likely to be useful on another rifle later if desired.
Best of luck in your search!