I am getting the Nikon D3300 camera and it comes with a 55-200mm VR lens. Will that lens be good for taking pictures of people snowboarding? If not, what would be a better choice?
It depends on the distance you'll be taking pictures from. If you are going to be close to the action you'll need a wider lens (smaller focal distance value). Otherwise, if you're taking pictures from a distance you'll be fine with that.
You should ask someone that has multiple lenses if you can check them out to see the efect.
Take into account that the camera you mention has a crop factor of 1.5 so the actual widest focal length of that 55-200mm lens is 55*1.5 or 83mm which is a tele lens. As long as you can keep your distance that might work.
However it doesn't look ideal to me. For snowboarding you often want part of the environment, snow flying in the air and maybe even landscape. That will be hard with a tele.
Also a nasty side effect of the tele is that you'll need faster speeds to freeze action.
Can't you get the double zoom kit or the one with the 18-55mm? That's a better all-round lens than the tele. Purchased in a kit these lenses are cheap so no brainers. Bought separately they get a little more expensive and I wouldn't advise these.
Once you know your preferred focal length (and you're convinced this is your thing) you can always upgrade to a fast and sharp prime. These kit lenses are no good to reveal the true power of that magnificent Sony sensor.
I'd assume you might be doing some video too. And you've seen GoPro videos no doubt. Note that GoPro cameras are using very wide lenses. They make it easier to have more in focus, include more of the close up action, and people are used to that look.
OTOH, as noted, if you are 50 meters away taking shots of someone else in a competition then you need the longer lens. Which is why "interchangeable lens camera." So you may need two, although I'd start with the 18-55mm and just crop to get tighter. Longer telephoto lens are generally slower, and getting past mediocre performance gets spendy fast. Those folks on the sidelines you see at sports events with big lenses on tripods are all sporting equipment that costs as much as a good car for the sort of photos you're possibly contemplating shooting. So again, you'd get a better bang for your buck right now with the wider lens.
One can manage but why are you considering something that slow? Being long and dim, you will have trouble keeping snowboarders sharp. The VR does not help here because you need a fast shutter to freeze motion. If you are shooting from relatively short distances, a 24-70mm F/2.8 will be much more useful. For far away shots, I would go with a 70-200mm F/2.8. Professionals oven use heavy lenses which have a brighter aperture but those do not zoom, so I would not recommend them for someone starting out as it is much harder to frame with.
The more suitable lens if you are shooting up-close with a cropped-sensor DSLR is the 17-55mm F/2.8 which gives you a wide-angle but not as much reach as the 24-70mm which is why I would recommend that one first for snowboarding.
I shoot the D3300 mainly and have a bunch of lenses for it, I also ski a lot but have never brought the camera on the slopes. Here are some thoughts,
Generally speaking ski slopes are bright places, between the sun on the snow and generally clear winter days you don't really need to worry about low light performance for this particular application. You may lose some performance on really cloudy days but you cant control the weather and those days may be unpleasant to ride in anyway.
The real question is where you will be when you take these pictures. If you are going to be on the side of the trail somewhere or possibly cant get close because the park is roped off you are going to want a tele zoom so you can really get into the action from a distance. If you are going to be/can get right up to the boarder you can opt for a wider zoom lens. For longer distance the 55-200 will work just fine, I trust ken rockwell and you can find his very positive review on it here. If you are getting in close the kit lens (18-55) will do just fine. For what its worth the kit lens is a really great lens in its own right.
At first I would avoid primes, since you may be limited in your ability to physically move around its better to take advantage of a lens that is capable of zooming in and out to capture potential action across a wide area.
You really don't need to crank up the shutter speed that much to capture great motion in great clarity. I shoot a lot of birds and can freeze motion with the D300 really well down to 1/250 in good light. For the birds I shoot I typically use the Nikon 300mm 4.5 which I picked up used cheap. I would not advise this off the bat as its a full manual lens on that camera and will take some time to figure out how to get the shots you want since your meter will not work with it and its manual focus. On the contrary its a really great lens for the price and extremely sharp even down at f4.5.
On the note of focus you will find that the D3300 autofocus is good but leaves things to be desired especially when it comes to really fast motion. You can set your AF point and the kit lens should focus pretty fast. Worst case scenario you can put both the kit and 55-200 in manual mode.
Frankly the 18-55 and 55-200 gives you full range of lens coverage for a solid price. I would buy both and play around with them (they are cheap). The used market for Nikon stuff is very stable and if you find you don't like either of the two you can always resell it and re-coupe most of your cost.