For closer range deer hunting, you don't need an A/O scope, though parallax issues exists from one range to another. It's just not as critical at shorter ranges. Lower magnification is all you need, and in some instances may be even better. Same for coyotes. For closer range coyote hunting, you don't need an A/O scope either.
A deer is a large bodied animal, thereby being more forgiving of precision. However, once you get on out there, such as you suggested at 300-500 yards, things really change. Parallax is a real issue and can make the difference between a hit or miss, or a wounded animal. Coyotes are even smaller targets, making it more difficult to connect with a killing shot at longer ranges.
Taking both deer and coyotes from close ranges to extended ranges, with a scope that does not have A/O, is asking a lot of the scope.
When calling coyotes, they can suddenly appear right on top of you, or they can hang up 300 yards away. Many times you don't have an opportunity to correct for parallax, but it's nice to have it when you need it. That 300 yard coyote that's just sitting there, looking the situation over, might give you a chance to range him and make necessary adjustments. Precision shooting is what we are talking about in this case. A hard-charger doesn't allow time for scope adjustments, but generally they are close targets, making parallax less of an issue.
As to scope magnification, the 3x9 is the all-around basic deer hunting scope. For eastern deer hunters, it's probably the most purchased scope of any. That is a fine choice for such shooting, such as timbered and thick areas, to open fields. But, when you get to ranges like you are talking, even a 9X just won't cut it, especially for coyotes. It's difficult at best to place a bullet where you need it to go, even for deer, at ranges of 550 yards.
Pertaining to scope reticles, my opinion is the more "clutter" you have in a reticle, the less valuable it becomes in the heat of the moment. I'm thinking coyote hunting here. But, for precision shooting at extended ranges, when you have time to "think" and consider the shot, then the extra reticles (varmint) or aiming points "might" be worth having.
Whichever scope you choose, you need to put it to use in the field. Learn the trajectory of your particular rifle and load, where the bullet hits at various distances. Even the scope with the varmint reticles are just good theories on paper. You need to find out what YOUR load does and where the bullet impacts at various ranges.
If you are needing to make one rifle do it all for both coyotes and deer, at the ranges you mentioned, then my vote is to go with a scope that has parallax adjustment. When hunting, set the parallax to a distance of where you expect the coyote or deer to most likely appear at. Generally speaking, you will have more time to make scope / parallax correction on deer than you will on coyotes.
For me personally, for the various types of hunting and distances you described, I would go with the 4.5X14 with an A/O. That combination would give you a lot of options.
The Leupold VX-3 is a fine scope.