I am 20 years old and also in college. I started last summer with the 2 push mowers, trimmer and blower I already had. At first I had 3 lawns and just cut them myself but those people told others and they told others and so on. By August I had grown to 12 lawns and had been regularly paying a friend to help me since June. I charged roughly $25 per lawn and made pretty good money by the end of the season after gas, pay for the worker and repairs. Of course I also have a truck so its easier, but my dad did it when he was younger out of a station wagon.
I would look into a trimmer, maybe a cheap $80 Craftsman or something because having one of those will make your job look that much better. Same thing with a blower, just find a cheap one or just use a broom if you don't care about time. Too bad your down in Florida because I have like 5 trimmers I don't use.
Anyways, to get these lawns I made an appealing flier of the services I offered (I also played the poor neighborhood college student card) and I walked door to door in a 3 block radius. Doing that got me only 3 customers but that got my foot in the door and I moved forward from there.
Sorry for the extremely long post but I figured I could help because we were roughly in the same situation. Good luck!