Scripts and films are essential to any filmmaker's portfolio.
Since shooting requires a crew, budget, time, and work, I would recommend writing scripts first. That you can do by yourself. Remember that filmmaking is storytelling, thus understanding some screenwriting concepts is valued. Although your first script probably won't be a master piece, you have to start somewhere. With time, you should hone your craft and produce better pieces.
An alternative to shooting and writing could be taking still pictures. I don't know if you're applying to universities or film schools, but some committees accept portfolios with photographs. Experiment with lighting, perspective, color, shot sizes... Shoot on different locations and different times of the day. Be critical of your work and select your best photos. If you are applying to a school, always check their portfolio guidelines and requirements.
Eventually, however, you must shoot short films. Give people a sample of your preferred position whether it may be a cinematographer, editor, screenwriter, director...
Good luck,