Adult piano students, your practice plan ideally includes the following items:
Technique. This should include scales/chords/arpeggios. It’s important to note every time you move to a new piece or item in your practice session, if you change keys, you should practice the relevant scales/chords before starting your work. Warmups may also include exercises or etudes.
Assignment from a “method book.” You can think of this as the “how to” guide to playing the piano. There are a number of method books written specifically for adult students. At my studio, we use several of these books in tandem in order to continually reinforce concepts. I typically continue with at least some form of method book up through the intermediate level. William Gillock is my absolute favorite composer in this regard. His collections include short pieces through all major and minor keys, from the earliest levels through late intermediate and even advanced levels. His pieces reflect all style periods and are absolute treasures. He also composed a number of jazz and boogie woogie pieces, duets, and popular piano arrangements-- truly something for everyone. All our early level students also work to complete Faber Adult Piano Adventures Books 1/2. We supplement with others, as I’ve mentioned, but choices in these vary, depending on the student.
Practice suggestions specific to repertoire pieces. Repertoire pieces are oftentimes outside the normal learning learning sequence and likely are more difficult than what you may be working on in the method books. They will take more time to learn and usually require some extra coaching from your teacher. At my studio, we usually work on one or two repertoire pieces per term. These are often performance pieces.
Sight reading assignment. Sight reading is just that-- something the student can read with no coaching from the teacher. These pieces are not practiced, per se, though the student will spend time analyzing these short pieces before playing. (As a general rule, that’s always appropriate, no matter what you’re playing.) It’s important to have graded material and for these assignments to be relatively short pieces, in my opinion. For early level sight reading, I find Jane Bastien’s MultiKey Reading really fits the bill. There are lots of books devoted to sight reading. I suggest you make sure whatever you choose takes you through all major and minor keys. If you find you're having to "decipher" the music, it's too advanced for sight reading purposes.
Theory. If you’re working from a good method book, such as the Faber Adult Piano Adventures books, theory will naturally be a part of your music education. If you’re not working from a method book, you’ll need a teacher to help guide you with theory.
Optional: Learning to use lead sheets. One of the reasons I prefer the Faber series is students explore working with lead sheets early on. Guitar players often read “tabs,” which are chord symbols. Pianists can do the same, reading chord symbols by using lead sheets. At a very basic level, this helps students better understand how music is constructed. If students choose to further develop this skill, they learn how to “arrange” songs to suit their own tastes or perhaps use this skill to start composing their own music.
If you're working independently, I suggest you try to incorporate these elements into your weekly practice plan. Using a quality adult method book or a highly rated piano app will best serve you, in my opinion. If you're working with a teacher, it's likely your teacher either writes the practice plan for you or makes suggestions for you to note in your journal. If you're working with a teacher who doesn't advise you on practice approach, I suggest you ask for specific guidance. (If I may be so bold as to say so, good teachers will always give weekly suggestions/assignments.)
Lastly, I think it's important to remind everyone to really follow the practice plan closely. It's easy to just sit down and play the piano in a way that may be unfocused or even sloppy. I like for my own students to be task-oriented, to follow their practice plans precisely. I never make recommendations as to how long they should sit at the piano. As a matter of fact, many adults have some degree of neck/back discomfort or pain and sitting for too long can exacerbate this. Students who have other physical discomforts should also avoid extended periods of time at the piano.
One last thought: I totally encourage everybody to play piano for pleasure by playing songs you already know or that you can sightread for fun, but I would consider that "play time" and not "practice time." By all means, play on!