First, Florida doesn't have "Unemployment" we have "Reemployment" - and that's the attitude you'll have to understand when dealing with the system in this state. I did it for 26 weeks, so I have 1st hand knowledge...
http://www.stateofflorida.com/articles/florida-unemployment.aspx
from the website linked above;
Keep Seeking Employment
Also when you claim your weeks, you will have to report your efforts to find a new job.
Florida unemployment laws require you to contact five potential employers each week in order to maintain benefits, so be sure to keep records of each one, along with the results of your contact, the website or email address used, the employer's telephone number, and the employer's name and address. You can use the Employ Florida Marketplace to help you in your job hunt; it has thousands of jobs you can search and apply for.
If you are unable to make five contacts in a week, you may be able to satisfy the requirement by meeting a representative at your local One-Stop Career Center. If you refuse an offer of suitable work, you are liable to lose your benefits.
Employ Florida Marketplace:
http://www.employflorida.com
TIP: Send out a resume a day, M-F, to a job for which you are qualified. Do it as soon as you wake up, and keep a word doc where you store the contact and job info.
As far as submitting your initial documentation, I would suggest doing it in person. The electronic tool doesn't inspire confidence, and it's worth a day sitting in the re-employment office so you don't have to worry about any delay in benefits.
good luck!