Taking a broader view
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For DSLRs, lenses from 21mm and down are usually considered ultra wide. As prime lenses they cost a bit more but are increasingly accessible in zoom format usually as kit lens that come with the camera.
Some people do not appreciate their flexibility, and some use them in ways that exaggerate unnecessarily the distortions of the lens.
1: To reduce distortion in landscapes, keep the horizon in the middle of the lens. Otherwise you may get bowing at the edges of the frame.
2: If you do take portraits with a wide-angle you should step back to avoid larger than normal noses. It’s possible to take brilliant portraits this way, but if you are too close the effect is comical. An interesting angle is to shoot someone facing you and pointing at you (like the famous WW I Kitchener Poster or the copy cat Uncle Sam needs you poster). For maximum impact your depth of field should extend from the tip of their finger to their eyes.
3: Taking a picture of anything tall, like a building, unless you aim at its middle point, will make it tilt back and the bottom will widen (you can correct this is in some software by using perspective control, but unless you have a lot of space around your subject you will crop out parts of your subject). Without software the only solution is to get on a roof or balcony and make sure the center of the building is the horizon line in the frame (not easy with the skyscrapers).
4: Your landscape photographs will probably need something in the foreground to build your composition. This is one of the places where leading lines, or some balance in the photo between foreground and background matters.
The photograph at the top was an effort at close-up photography with a fish eye (10.5 in Nikon DX format or 15mm in 35mm format). Interesting, but not spectacular; you get the idea, experiment!