Finding a really beautiful, relevant and memorable avatar for your own page is, scary to say, a titanic work. And how not to get in the eyes of the public a label of "hypertrophied vulgarity" and "excessive enthusiasm for photoshop" - this is a task out of tasks.
The easiest way is to put a picture on the page that depicts not you, but something or someone that reflects your current essence. It is desirable that the image be without text. The text immediately adds absurdity to the avatar. Let everyone find on it something that suits you, without words.
If you do decide to put yourself on the profile picture, first take good photos with a professional or semi-professional camera. It is advisable that after all someone photographs you, and not yourself. And forget about the arm-length shots that are stored on your phone. Choose a scenic location in the city, rather than your own apartment, as a filming location. Dress nicely, not vulgar. Choose an angle from which you look good (again, good, not vulgar!). Everything in the photo should look harmonious.
Then it's up to processing. Don't get too carried away with Photoshop. Beautiful avatars always look natural. Do only color correction, crop what is not needed, and retouch the face to a minimum, if necessary.
If all this is for nothing, seek help from a photo studio. They will do everything for you.