IMHO fixed mag scopes make no sense for in the field use, they are way too limiting in use. Hence the invention of variable power scopes.
Leon, 
well said!
▪When my shooting is at ranges that often change — variable magni is the answer.
▪When I don't want to switch scopes all the time — variable magni is the answer.
▪When I choose not to own a lot of guns (not going down the "One-gun-for-each-type-of-shooting") — that is, when
I want an all-round gun with an allround scope — variable mangi is the answer.
The magnification at the BOTTOM END — for an allround scope I think this really is not so much about the magnification — and
more about the field of view (FoV): For
quick target acquisition at close range shots when stalking I need to be able to get the quarry into view
quickly. That critter at 11 yards won't give me much time...!
Personally, I find a
FoV of 30ft at 100 yards to be sufficient. 25ft is already getting a bit tight.
For a 30ft FoV (at 100y) you'll
need a bottom end of 4x or 3x, usually.
Do check the FoV in the scope specs though, because I've seen scopes that (at 3x) had a FoV of 42ft — whereas others only had 26ft!).
➔ Once I determine the bottom end of the magni — I realize that the options are much more limited. That's why the bottom end is the first decision I make.
Then I determine top end magni.
The magnification at the TOP END — for an allround scope The top end depends on whether I want to
(1) only see the target for hitting it —
(2) or if I also want to
see my hits....
For (1) the magni doesn't have to be very large — unless your eyes have been getting up in years.
For (2) you'll need much more magni.... And/or a scope that has pretty good glass (=$$).
Personally, for my not-super-young-anymore eyes I'll need
16x minimum to barely see hits at 100y paper targets — in mediocre lighting conditions. Your mileage will vary....
However, it'd be nice to get 20x or 24x magni, for those longer shots, or to see my hits better. And they say, "Aim small, miss small."
Availability — in the price range of $500 and under ▪Looking at what scopes are out there
that fit those bare minimum requirements.... — there are plenty of
4-16x out there.
▪
If my emphasis was a bit more on close range hunting — I'd prefer a
3-16x or 3-18x — this shrinks the choices a lot.
▪
If my emphasis was a bit more on long range, or my eyes need some extra help — 4-20x or 4-24x would be my preference — the amount of choices is smaller yet than the 3-18x.
Matthias
Attachment 1: Here's my
Scope Specs Table for scopes with 4x or less at the bottom end, and 16x or more at the top end.
View attachment 1586965409_10233580505e972ba11f7502.96544711.pdf Attachment 2: Here's a
visual comparsion of different magnification ranges in a simple table.
.
Such a deep rabbit hole.... 
