If you have the time to practice 30 minutes a day, I think it would be okay to meet once a week. I meant that if practice time is seriously low to the point where you wouldn't be making sufficient progress after a week, then I'd meet every 2 weeks. Usually what happens in a lesson (for me) is that I play the piece, the teacher gives ideas on phrasing, articulation, advice on fingering (aka technical issues), attention to dynamic markings, weight distribution, wrist positioning, etc. Each of these topics can take several minutes to explain, demonstrate, and have the student repeat the form of musicality being discussed. We also talk about dynamics and expression not written into the piece. With all levels of music, it is not an uncommon practice to have the student learning more than one song at a time, so multiply that by however many songs you have and your 30 minutes will fill up really fast! Because my teacher is very excellent at what she does, I feel that the hour lessons we have are definitely worthwhile. Every time we meet I come out playing different than when I entered, or at least with different ideas on how to go deeper with the music for next time.
I'd recommend finding pieces outside of your music books that you'd like to learn. Generally speaking, a series will have a fair selection of songs, but if there's something you'd really love to learn and you feel you're able to learn it, bring it up with the teacher and they'll be able to tell if that's within your range or not. It also gives the teacher some ideas on what kind of music you like to play and helps him/her find other pieces for you when you need a break from the books.
"His name ought not to be Bach (brook), but Ocean, because of his infinite and inexhaustible wealth of tonal combinations and harmonies."