A 3-9 x 40mm variable is the most popular type of scope. Of course, the variable magnification (from 3x to 9x)...gives a lot of flexibility. However, most people NEVER have a need for anything above 6x. For hunting purposes, you'd do better to keep the magnification modest....say about 1x, per 50 yards of distance. Thus, for shooting at 50 yards...no magnification is needed.....for 200 yards...about 4x is all that most people ever need. The reason to keep the magnification on the "modest" side is that, with increased magnification, there is always a corresponding decrease in the field of view....and visual depth of field. 9x, in most cases, at say 200 yards, will narrow the field of view so much that, if the animal moves before you shoot....you may have trouble finding it again, in the scope. Even 3x is a bit much at 50 yards. Also, the higher the magnification, the more the optics will magnify small movements of the rifle, such as if shooting off-hand. A low-power scope will not produce nearly this effect, so that is also why I suggest about 1x per 50 yards of distance.
So, I would tend to suggest a low power scope, if your usual hunting distances will be 200 yards or less. A fixed 4x would be fine for all but less than 75 yards, roughly. Given the increased flexibility of a variable, the 1.5 -4.5x (or 1.5 - 5x) will cover 95 % of the hunting situations you are likely to ever encounter, plus be usable at short ranges, such as 50 yards. Such a scope would allow you to very comfortably, (if your shooting skills allow), to range out to at least 250 yards. The vast majority of deer in the US are taken at 200 yards or less....in fact, more than 50 % at 100 yards or less. So, I would second the suggestion for a 1.5 - 5x scope, or something similar.
As for objective size, this is another area where many people overdo it. A 40mm objective (or larger), simply isn't necessary unless one is using above 6x magnification. Exit Pupil is the important factor...and should always be considered when purchasing a scope. The larger the objective size, the higher the scope must be mounted, which can reduce accuracy (and certainly can make shooting less comfortable, depending on the stock design). Exit Pupil is the true measure of the light transmission of any scope - so forget about the claims of "93 % light transmission", etc., that many scope makers claim. The usuable light (Exit Pupil) is determined by dividing the objective size (in millimeters) by the magnification. So, a 3-9x x 40mm scope has exit pupil numbers of 13.3 to 4.4. The human eye cannot use more than 7mm of exit pupil (and that is when eyes are young)...and usually 5 or so, from about 40 years of age. So, you see, a 1.5 - 5x x 28mm scope, will have an exit pupil range of 18.6 to 5.6...perfectly adequate for the vast majority of hunting situations. I would, therefore, suggest, in addition to the 1.5 - 5X specification, that you choose a scope with a 28 - 32mm objective size, maximum. This will keep the scope lighter in weight....it can be mounted lower (leading to better shooting, very often)...yet will still cover 95 % of your possible needs.