On the driving from Miami to S. Cal. Be very aware that this is a VERY long trip. Just how long are you planning to take for this drive? And, what do you plan to see and do along the way? At what season? If you drive pretty much straight through you could make it in maybe a week, but, what would the point be? Also, as mentioned above, it can be quite costly to rent one way.

You might want to think about more flying and less driving. How about something like, tour S. Florida, fly to Albuquerque, tour New Mexico and Colorado, fly on to L.A. If you like, you could add some time in, say, Chicago. Such an itinerary could easily take a month.

By the time you drive from Florida to L.A. to Vancouver, you will be car crazy.

Europeans very often vastly underestimate North American distances when they plan drives. I recently had some UK visitors who planned to drive from L.A. to SF for a day trip and were amazed to discover that this was impossible as it would have required close to a thousand miles in one day.