you got yourself the best motorbike ever made there are many variations of the honda cub it is the oldest motorbike still in production also the most sold ever (over 50 million)....been made since the late 50's or early 60's and the cub has gone thru many updates but is more or less the same bike. It broke the US market and got honda where they are today..remember the old commercial "you meet the nicest people on a honda"
It is technically a scooter not a motorcycle...I guess legally speaking in CA it is a motordriven cycle.
If you have problems with it call Battlescooter in Sunnyvale. They are the ones that specializes in Japanese scooter and more specifically Honda scooters and motorcycles. Can get you parts for it if you need as well.