Congrats on the new bike! I just got my first bike about 3 months ago. 2002 CBR600F4i. Oh boy do i love it. So much so that I already have almost 5000 miles on it! I have been to the track. If there is one near you and you feel confident enough, do it, you will learn so much more there than you can on the street. For anyone in the PA, WVa, OH, Maryland area, hit up route 50 and surround roads in WVa. There are just some amazing stretches.
I don't know about that whole, "dropping it makes you a better rider" thing. Just the thought of dropping mine encourages me to be a better rider, that's all the motivation I need!