I think if we can learn how to make our own artist/portfolio website/page, it will be a good idea. (After we learned those basic skills of building a website/app.)
Personally, for the design part I would like to learn more about some interesting knowledge about the visual looks for app design/web design. For example, how many pictures in one page/screen is the most comfortable look for people’s eyes? What kind of colors will stimulate/attract people want to read more?
I really like the design of Instagram, SSENSE (a shopping web), Celine, and Pinterest. Clear and compact looks; practical functions and easy to use are the main points.