Repertoire
I think that it’s important to start building a repertoire of piano pieces that you can play by memory as early as possible. I’ve often heard pianists say that they can’t play by memory but I suspect that this is because they haven’t made a conscious effort to do so. The best way to memorise a piece is to focus on small sections at a time, study the sheet music, try to picture the music in your mind and then, crucially, put the music out of sight while you play. If you find it difficult then try an even shorter section, you will probably be surprised at the progress you can make if you focus on very short sections at a time. Once you can comfortably play the first section by memory then try the second and so on until you have memorised the whole piece. When you have memorised a few pieces then I would arrange them into a set list so that you are always able to sit down and give a recital at the drop of a hat.