If I can only use one, should I choose a UV filter or a lens hood?

As you know, distant mountains are most often veiled by a bluish haze. This is a vapor cloud that often spoils the beauty of the vista. The same is seen when we fly; the clarity of our aerial image is tainted by the same phenomenon. What is happening is: The UV and violet light has the shortest wave lengths of the light spectrum. They can and do skip past some tiny particles of dust and water vapor. However they have a higher probability of colliding than the longer frequencies. When collisions occur, the UV light from the sun is scattered. Photographic films are super sensitive, and will record this scatter as a thick haze.

We can reduce the harmful effects of UV scatter by mounting a UV filter. Now the scatter is only seen if the light must travel many miles to reach our camera. In other words, the UV filter is worthless if the subject is a mile or less away. You should also know the popularity of the UV filter is mainly the product of camera shop salesman trying to line their pockets.

The digital camera also has sensitivity to UV light. Because the image sensor is delicate as well as precious, it is protected by a thin transparent cover glass. This allows the sensor to be cleaned when and if it accumulates dust etc. Now this cover glass is also a UV filter. That makes mounting a UV filter to the camera lens, a redundant act.

Let me add that the lens shade is used to shield the camera lens from stray light that originates from bright objects outside the field of view of the camera. If a lens hood is not used, there is a high likelihood that some of this stray light will intermingle with the image forming light rays. When this happens, optical flare is induced as well as ghost images. Flare robs contrast and ghost images are creepy. The lens hood is worth mounting, always.