Another point for the novice scope buyer to consider is that magnification in itself is not the advantage of the scope sight. The advantage of the scope is that the reticle and the target appear on the same focal plane, where with irons, if open, the eye must line up 3 different objects, rear sight, front sight and target. The eye can only focus at one focal distance at a time, so the drill is to attain a rough sight picture, line up the front and rear sight, confirm the position of the front sight on t he target, then focus on the front sight. An aperture sight is a bit better in that the shooter ignores the rear sight and only looks through it, then after confirming the position of the front sight on the target, shifts focus to the front sight, and breaks the shot. A scope does away with all that, as the reticle and the target both appear in crisp focus.
The purpose of magnification is to allow you to see your target. A small target or a target which is farther away requires greater magnification to see, but conversely, a large target, or one that is closer requires less magnification to see equally well. There is no free lunch, and as the apparent size of the target becomes larger, the field of view, that is the width of your vision becomes smaller. An extreme example might be that you can only see the eyeball of the elephant, but that is little help because you can't see anything but a grey mat in the sight picture. It is much more useful to see the entire elephant, so you can choose where to shoot and decide when you should shoot. The other side of the coin is attempting to use little or no magnification when shooting prairie dogs at a quarter mile. The target will be all but impossible to see, and will, in all likelihood, be hidden behind the reticle.
Target size and range are the primary considerations when purchasing a scope, but the tendency is to choose too much scope for what you will realistically need in the field, and could result in missed opportunities. The reason for this is that many more rounds are fired at targets on the rifle range than at game. On the rifle range, our target often has an aiming point little bigger than a squirrel's head, and this unrealistic target too often leads us to putting varmint scopes on our big game rifles.
The OP is interested in 3-9Xs and 3.5-10Xs, and these do tend to be versatile performers that are suitable for big game rifles, but for 8X, 9X, or 10X to be really useful suggests wide open spaces. Even then, the least magnification should be selected to allow a hunter to react to action which may occur at very close range, where there is no time to select a lower magnification, and where the game is lost in the view of the high power setting. If a long shot is presented, the game is unaware of the hunter's presence, so he'd has time to select a higher magnification.