Why not start with the Bach pieces you mentioned? That way you can get some feedback that may be supportive or helpful. Everything is more difficult as soon as you press the "Record" button!
I'll start with those, but I'll need some other pieces for later on.
Learning pieces within minutes, hmmmm.... You have to be very experienced for that. And even then, it won't work. However easy, the music needs to grow on you.
Let's just say sometimes I have time to play an entire day, sometimes I can't play for weeks. I've played Bach's fugues and preludes, entire Beethoven, Mozart & Haydn sonata's before, but that was 5 years ago, when I was still following piano lessons. So I've got some technique, but I don't have time to take several months for 1 piano piece. Anyway, I'm looking at Chopin's second nocturn now. It's a bit more difficult than I'd wish, but I think I'll find the time (for now) to work this one through.
So it's not a matter of choice or laziness, I just don't have that much time to practice classical music.