I love fixed power scopes, especially for deer hunting. Lighter, less moving parts, relative reticle distances fixed, simple, and they just scream rugged to me. Personally, I don't think you need more than 4x for shots at deer under 300 yards. Don't make this more difficult than it is, I now fit just the optic needed to get the job done on a rifle and no more.
I have a pet 30-06 I do most of my rifle hunting with. It is topped with a 3x9-40mm and would not be considered a tack driver. The scope is on 4x and I rarely move it. I wish it was a fixed 4x. I can say this because I took at doe at the max range I have established for this gun and did so on 4x, never considered cranking it higher. The range was a bit over 250 yards. No trouble knowing the crosshairs are on my target at that distance at that power. I now want to simplify the rifle with a fixed power 4. No need for the variability.
With the accuracy you need to shoot to kill deer the high magnifications are not needed. It doesn't help. It will, however, amplify your wobbles and nerves and make you feel less confident. It really doesn't change how precise you can be. Learn your gun on one magnification and build that familiarity and confidence.
My muzzleloader has a fixed 2.5x that I love.
I'm building a longer range deer rifle, a .270. It will get a fixed 6x.
The best advice has already been given. Whatever you do, get the best quality you can. My suggestion is just enough power to fit the rifle. Get the higher magnification in the spotting scopes and binoculars. That's what those are made for! Scopes are just for delivering a bullet into the kill zone.