I'm trying to decide if the right hand plays all the noters in the treble Clef and the left just bounces around between single notes, or (since the steps on the chords in the treble clef point down) does the left hand do a single note and then two notes of the chord jump kinda thing?
Full 1st page. Click for full size.
You can play whichever you find easiest, but the piece looks like it's trying to teach you elementary stride piano, which comes from ragtime music of the late 19th, early 20th century.
In this the left hand maintains this constant bass/chord/bass/chord pattern, whilst the right hand can go off to do something far more adventurous. Listen to Scott Joplin's The Entertainer for a well-known example of this form.
Probably the most famous version is the one from the movie, The Sting
Technically, your piece is written in three 'voices' one in the bass clef and two in the treble. That's why the treble clef voices show the note stems running in opposite directions & why there are 'extra' rests, which belong to the middle voice, the chords.
What they never tell you is which hand to use - that's up to you, but in this case I think it looks like they want you to practise your stride. That's probably why the melody is simple & varies really only rhythmically - to build independence between your hands.
This appears to be a simplified arrangement. The original likely uses a stride pattern (jumping your left hand back and forth over multiple octaves, often very quickly) with a more complicated right hand that makes it impractical to play the inner voicing as well.
Stride can be very challenging so with a simplified right hand it makes sense to play the inner voicing too while the left hand can just sit in the lower register without jumping back and forth.
This is indicated by the way it is notated. There is a full rest between each left hand note where the inner voice could go and placing the notes on the bass clef would eliminate the need for ledger lines while also getting rid of all the additional rests. The score would be much simpler if the notes were to be played by the left hand. The additional complexity is used to indicate the notes should be played with the right hand. You will most likely find this much more comfortable.
That said, if you want to try playing them with your left hand, I see no reason why you shouldn't. It might even be a fun challenge and make it more fun to play!
Traditionally, l.h. plays dots from the bass clef, r.h. those from the treble clef. And that will work here, too. There's nothing too jumpy for l.h. then. You could play the dots with stems down using l.h., but that's almost stride piano - not the easiest! The reasoning behind the stems up/down on the treble clef is that the stems up are the 'tune', while the stems down will be played slightly quieter, as accompaniment.
So, keep the hands and clefs separate, as writ, and it'll work just fine.
Incidentally, the top line (extra treble clef, so far empty), will eventually have a vocal line, which will start after the intro, perhaps more bars later than shown here.
