A. Your 18-55mm zoom lens is a sharp one when used properly. If you are not getting sharp pictures, your best investment may be practicing and refining your shooting technique, not a different lens. In most photos, lack of sharpness comes from (1) not focusing on the subject, (2) camera movement during the exposure, or (3) subject movement during the exposure. Only at the absolute limit with large prints and a detailed image is it likely that the optical characteristics of the lens are causing what you see as problems with sharpness.
Focus on the subject depends on what autofocus mode you are using, and making sure that mode lets the camera focus on your subject before you take the picture. The 18-55 mm zoom does not have very fast autofocus, so you could be challenging that lens with your technique.
Concentrating on holding the camera steady is very important at speeds slower than 1/60 at 55mm, and speeds slower than 1/30 at 18mm with your lens. You can't be careless about this, or camera motion will cause fuzzy photos. If you're using VR, that can help down to about 1/15 at 55mm and 1/8 or even 1/4 at 18mm.
However, VR won't stop subject motion. To stop subject motion you need to take pictures at 1/30 second or faster for people who are relatively still and not talking, or 1/60 to 1/125 for people who are moving slowly or talking. For people who are talking or gesturing in closeups, you need to use 1/250 or faster to stop their motion. You can catch the peak of motion at 1/60 or 1/125 in closeups, but at 1/30, most of your shots will have some blurring from subject motion.
To get the sharpest pictures with this lens, you need to hold the camera steady by bracing yourself and your camera and controlling your breathing, and to use an ISO rating and shutter speed on your camera appropriate to the motion of your subject and the amount of zoom you are using. You will be trading off between stopping motion of your subject and loss of image quality with higher image noise at higher ISO.
If your problem is action shooting in dim light which results in subject movement, then learning to use flash, or using an f/2.8 or faster lens may help you get sharper photos by allowing you to use a faster shutter speed. The f/2.8 zooms and fast AF-S prime lenses will also provide faster autofocus response than your 18-55. What shutter speed and which faster lens you need depend on what you are shooting.
For most outdoor daytime shooting, your lens should be plenty fast for most fast action - just use a setting that gives you a shutter speed of 1/500 or so.
The budget way to a fast lens for your indoor shooting with the D3100 is the 35mm f/1.8G AF-S DX Nikkor. This lens has a great reputation and is around $200. The angle of view of this lens is not very wide, so to me it's quite limited. Nikon needs to produce a wider angle fast lens for indoor shooting with DX cameras. See the characteristics of that lens at the link below:
http://imaging.nikon.com/lineup/lens/singlefocal/normal/af-s_dx_35mmf_18g/index.htm
A preference is a faster zoom lens like the 17-55 f/2.8 zoom, which can be used for general-purpose indoor shooting, which typically allows you to use a shutter speed of 1/60 or faster with indoor lighting with ISO 400 or ISO 800. For portraits, I like to use the 50mm f/1.4 G lens, which gives nice subject separation with its narrow depth of focus.
If you're shooting sports indoors a ways from the action, you will need a longer telephoto zoom, like the 70-200 f/2.8 zoom for over $2000, and a higher ISO, like 1600 or 3600, to allow you to shoot at a higher shutter speed of 1/250 or 1/500 at least. You could also use a lens like the new 85mm f/1.4 AF-S lens to give you even more light, but achieving focus on the action at f/1.4 can be quite challenging.
