In order to make an educated decision on what kind of scope best suits your needs, many things effect your choice; One is the 'Magnification' and 'Objective.' When the size of the scope indicates that it is a 3-9x32. The 3-9 is your magnification. Meaning you have the option of magnifying your target from 3 to 9 times its normal visual size. 4x32 would mean it was a fixed magnification scope at 4 times magnification. The 32 is scope objective expressed in millimeters.
The magnification of your scope effects how much you can zoom in on your target - how big you can make your target look. Things like the caliber of your gun and your purpose when shooting have a great effect on what magnification will suit you best. For example if you own a .223 or other 'assault rifle' type weapon you may want to go with less magnification because most of your shots will not be as long as maybe a 30-06 or .308. Generally up to 9x magnification if great for assault rifle rounds and anything more may (but not necessarily) be too much magnification. As far as shooting a target or hunting rifle, it is completely up to how far you want to shoot. Obviously more zoom means you can have a bigger picture of your target -- but be careful because the more zoom you have, the harder it becomes to steady your shot. FYI: The standard for a military sniper scope is fixed power 10x32.
The Objective is the size of the lens at the very end of the scope (the end that points toward your target). Depending on your shooting experience/ preferences you may choose a larger or smaller objective. There are two main reasons for having a larger Objective. First: a larger objective gathers more light into your scope. So sometimes larger objective can assist you when you are attempting to shoot in low lighted conditions. Second: generally the larger your objective the more 'field of view' (FOV). Many hunters like a larger objective because they can glass the field better with the wider FOV. However one disadvantage is when you have a wider FOV your target is a smaller percent of your overall vision. Often this makes it difficult for some shooters to stay focused on the target.
It is hightly reccomended you read "The Exit Pupil" to find out the inportance of its relationship to the focus of your scope.
Hope you found this helpfull. Cheaper Scopes