Lens for my Nikon D3300?

I'm using this camera for a variety of purposes (videos, nature photography, sport photography, etc), so I need a lens that will be fit for all of them! Right now I'm using the lens that came with the camera, which is a DX VR AF-S NIKKOR 18-55mm 3.5-5.6 II. It works alright, but for me, I need something with greater zoom capabilities. I'm looking at getting another lens with a max focal length of 200mm. I'm a college student (film school), so I do not have a ton of money to spend. Basically, I'm wondering if I would be better off getting an 18-200mm lens and selling my 18-55mm lens, or just getting the cheaper 55-200mm lens and keeping my 18-55mm lens as well. I know there are tradeoffs in both scenarios, but the bottom line is that I need a lens with better zoom capabilities. I'm on a budget, so I don't have many options, but I feel that one of these two would be my best bet. Please give me some advice as to which direction I could go and any suggestions are appreciated!

I'd go with the 18-200. The reason being, carrying two lenses means that Murphy's Law will get you. You will have the shorter zoom mounted, you will see a great shot - and it will need the longer zoom!

If you do the kind of photography where you can afford to take your time (landscapes, etc) then you can get away with having two lenses and changing them where needed, but if you shoot things which require quick decisions (sports, etc), then a single lens with a longer range is going to mean you lose fewer shots. As you state that you shoot a variety of things, the 18-200 could be what you need. It is said to be a jack of all trades / master of none type of lens, but as you shoot a variety of subjects it could be suitable.

(There's also an 18-300 if you really want to get some zoom).