Actually, I'd like to try/do both (if given the chance). Haha. I plan to take my camera for my future hikes specially this upcoming summer.
I'm currently watching youtube videos/ reading articles re: landscape photography. They were mentioning numerous lenses for such use. I honestly have no idea which one do I need specially considering my budget constraints and relative lack of experience in photography. Hehe.
Thank you for all your inputs guys! I appreciate it.
First off i'm going to ramble on here with lots of bad grammar and run on sentences. I apologize for that up front.
As others have suggested above "landscape" can mean different things to different people. I think most people automatically assume "wide angle" lenses are best for landscape and that is true for many situations especially when you want to emphasize the foreground, for example ocean scenes where there is extreme depth of field all the way up to the wet rocks that seem to pop out of the foreground. However if you are a person that thinks of "landscape" as a long panoramic scenes with a grand mountain range then usually wide angle lenses do not work well for that as they push objects farther away to cram more into the frame making the mountains seem small and insignificant. Using a much longer telephoto lens to compress the image and stitching them into a panorama works much better to capture the mountain range as we perceive it with our own eye.
Now if you consider what I said above combined with the knowing that the vast majority of landscapes are shot stopped down to a smaller aperture such as f11-16 for good (but still sharp) depth of field, and that most zoom lenses even of the budget variety (kit lenses) are still acceptably sharp in the middle of the aperture range then generally speaking there are literally TONS of great budget all purpose zoom lenses out there that give you the flexibility to shoot wide or long with good quality. Keep in mind these lenses I am speaking of will probably be variable aperture and not be very suitable for low light situations where a tripod cannot be used. (oh I should mention in case its not obvious. A tripod is a must for landscapes!!)
Now bring the milkway and stars into the mix. Everything I said above you can just through straight out the window, all the rules change. With stars you need to be able to let in as much light as possible for as long as possible without the stars trailing in your exposure. In order to do that you generally need a lens that can shoot with a pretty fast wide open aperture such as 2.8 or better and you need the lens to be wide (especially on a crop sensor camera like your D3100). The wider the lens the longer you can expose without trailing the stars to the point that they become little blobs or streaks.
So to really answer your question, there is no "best" lens. There are always trade offs and sacrifices that must be made for different situations. The fewer sacrifices you make with your lens purchase the exponentially higher the price tag rises. In the world of photography the words best and budget don’t really get along. If you are really serious about landscapes my recommendation is that you will probably want two lenses. I'd start with the Tokina AT-X 116 PRO DX-II 11-16mm f/2.8 as a really good semi flexible wide angle lens good for stars and general wide angle landscape applications. This lens has been noted many times for it capability of capturing great milkyway shots. But for more intimate landscapes and panos i'd recommend something like the Nikon 55-200mm f/4-5.6 VRII. The wide angle Tokina I mentioned can be bought new for about $400 USD and the Nikon zoom for about $150 USD. I'm sure can can find both lenses second hand in great condition for much less.
I should note I'm a Canon/Fuji shooter so hopefully some of the Nikon guys will chime in with there suggestions. I hope some of this was more helpful than confusing. LOL
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