I am interested to shoot fast balls such as golf balls and tennis balls to see their features such as speed, spinning and start angle. I am an amateur and only familiar with photographing though my Nex-3N where I change the shutter speed to see the fast objects but they become pretty dark. Next I would like to find a camera able to shoot high-speed objects -- does this mean that I need to buy a camera with wider lense to get more light? Or camera with some other features? Which criteria should I use in selecting such camera?
You can use any camera if you can have some control over ambient lighting. To achieve sharp pictures, you need
large DOF and
fast strobe or a very powerful continuous light (but I suggest the strobe way).
Large DOF is achievable with smaller aperture, and you can also control ambient lighting with that. The strobe will freeze the motion for you, and you will only have to be sure that the shutter does not interfere with the strobe.
The easiest is to do these types of photos in the dark, with BULB mode, and manually triggering the strobe. If you use manual focus and large DOF, then you will have your intended sharp pictures.
If you are shooting in natural light, you will have to see the max. synch speed between the strobe and your camera. Usually it is around 1/200 s. So you use Manual mode, set the shutter to 1/200, ISO 100, put an object to the position where you want to take the photo, and make a test shot. Then adjust the aperture and ISO as needed to have sufficient DOF/sharpness and to not clip in highlights. Do NOT open up your aperture to get more light, because you will have shallow DOF.
For a shot like this you need 4 things. First, you need the ability to focus on a quickly moving target or the ability to pre-focus on the spot where you plan to photograph. Unless you have a large budget, it will probably be the later as the former requires pretty expensive hardware ($3k+ probably) to really ideally handle high speed situations.
The second thing is consistent and preferably low shutter lag. Shutter lag is the amount of time it take for the camera to do it's thing from the time you press the shutter to the time the image is captured. If you want to capture a precise moment, you have to be able time the shutter very well too. If the shutter lag isn't consistent, then it is always going to be pure luck, even if it is consistent, relative to something taking a few thousandths of a second, it will still be long. Even Canon's top end DSLR has a 36ms lag, which makes a difference when shooting at high speed.
The third thing you need is sufficient shutter speed and lighting. In order to avoid blurring, you need a very fast shutter. In addition, the sync speed will make a bit of a difference since very high shutter speeds don't have the entire frame exposed at the same time, but rather the second curtain starts closing before the first finishes opening. This results in a slight diagonal angle to the capture of the shot, but the faster the sync speed, the more of the frame can be exposed at a time and the less angle you get. Similarly, the faster the overall shutter speed, the more light you need, but the less motion blur you get. Fast lenses can also help with this, but they are double edged as they also narrow depth of field and complicate focusing.
Lastly, you need either a trigger or luck and practice. If you have a way to reliably tell when something is coming, you can hook up a trigger to fire the shutter for you at timing far faster than you could normally control and have it account for the delay from shutter lag. When that isn't an option, you are dependent on your reflexes and your reflexes are probably not precise enough to regularly get a shot of the ball as it is getting hit with a bat or a golf club. Even with practice and fast/accurate reflexes, if you can get 1 in 20 fairly close, then you are doing pretty well. I think I personally get maybe between 1 in 50 to 1 in 100 that I actually really like. (Shooting on reflexes with a 5D Mark iii.) I don't get an opportunity to do action photography a whole lot, but I enjoy trying my hand at it when I can.