Is the slur telling me that I simply have to play it legato on all the notes on the treble clef and also when i transition from the C note to the G note (on the bass clef). Or is it telling me that I have to play all the notes on both staves in legato?
The first one is the correct answer. The bow is only for the upper voice. In order to acchieve this, you have to play the upper g from the last chord in the left hand a little bit shorter.
Since I am not allowed to comment yet, I need to add something to Tim's answer: Pop-piano is mostly played legato. But, note that even Chopin's standard way of playing was non-legato (In every place he wanted a legato he wrote a bow - and he wrote lots of bows). And there is a good reason for that: Using both playing-styles heavily increases the quality of the performance. Therefore: If there is a legato-bow play legato, if there is no bow play non-legato, if there are staccato marks play staccato.
Nevertheless, the book you are using seems not to care about legato. In my opinion, the bow must end at the c. This score would be a much better one:
The slur is indicating that the melody travels into the lower stave. I'd be inclined to ignore the printed fingering and play the entire melody with the RH. This isn't a terribly good bit of arranging. The priority seems to be maintaining hand position rather than serving the music. OK in elementary teaching material I suppose. Don't treat it with TOO much respect!