I have a Nikon d750 full frame and am wanting a new lens for low light landscape photography and low light portrait photography. I am considering either a 35mm or 50mm F1.8.
Which would be a better lens for my full frame camera?
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Oftentimes portrait photography and landscape photography are at odds, with portrait photography favoring longer lenses for good bokeh effect and landscape looking for wider lenses.
However, for a good general-purpose lens for both types of photography, you can't go wrong with a 35mm. Get a fast lens (wider aperture)-- an f/1.8 or f/1.4, whatever you can afford. A 35mm f/1.8 will still let you take beautiful portrait pictures, but also be wide enough to capture landscapes decently.
Hope that helps!
Unfortunately, there isn't really any good prime lens that will work well for both portrait and landscape. The goals of the two tend to be mutually exclusive, so any lens you choose will either give you good results for one and poor results for the other or mediocre results for both.
That being said, if you had to pick one of the two, the 50mm will probably server you better. It's not going to blow up the subject's noses too badly when shooting portraits (shoot a little wide and crop to reduce the effect even more) and provided you can get good distance you should be able to get a descent landscape shot with it. It also has the advantage of being several hundred dollars less than a full frame 35mm prime lens.
You can then use the remaining budget in the future when you're ready to buy a proper portrait lens (I use a 105mm prime for normal portraits and a 200 or 400mm prime for fashion work) and a panoramic head for your tripod (which I use with a 50mm lens mounted vertically when shooting digital for landscapes, though I prefer my 6x24 panoramic camera for that type of work).
Portraiture is an art form and there are no rules in art, you are free to follow your heart. That being said, if you are doing portraits for a living, your goal should be pleasing your client. Likely what your client wants is an image that is a close match to what he/she sees in the dressing mirror. In other words, an image that approximates the dressing mirror perspective.
How this relates to focal length: Many think, 105mm is idyllic portrait focal length. This comes from the following:
The typical commercial portrait will likely be an 8x10 inch image displayed on a mantelpiece. Likely this image will be viewed from about 3 feet distance. The dressing mirror perspective is achieved when the viewing distance is approximately the focal length multiplied by magnification (enlargement). To make an 8x10 from a full frame requires approximately 8 ½ x magnification. Suppose a 105mm lens is used. The viewing distance becomes 8.5 x 105 = 893mm ÷ 25.4 = 35 inches.
This is the origin of this rule-of-thumb, it is not engraved in stone, follow your heart.
As to landscape, most choose a wide-angle 28mm thru 35mm.