First of all, I would not use a handyman to do your roof. Personally, I would prefer someone that only does roofing. Like others answered here, get 3 estimates in writing.
In Florida, you need a specific Roofing Contractor's license to perform work legally, AND, to pull permits.
Only use a licensed contractor. Ask them for their license number and check it out on:
Ask these same roofers for a copy of their insurance policy. You can call the insurance company direct to make sure the policy has not been cancelled and is indeed in effect.
The proper way to replace a roof is to tear off existing shingles completely. Your contractor may need a dumpster. We used them all the time. Otherwise, it's a mess. Flat tar roofs can be torn off, too, down to the plywood decking. Both will be replaced with new roofs. If a contractor tells you that he will go right over your old roofs and that there's no reason to tear off the old one, keep looking for another roofer.
There are lots of problems with old roofs and many of them carry water between the shingles, bubble under the tar, or are hiding rotted wood on your roof decking/plywood.
So remember: Roofing contractor. Tear off old, put on new.
GOOD LUCK and let us know how your roof turns out.
Scott Miller, Realty Associates, Boca Raton, FL
Permits have to be filed with the county and I don't think a handyman would qualify. As an "owner" I think you can do the work so there may be a loophole.
I had a client who recently put on a new roof and she saved money by hiring a roofing contractor do the "labor" and then negotiated a spectacular deal on the shingles from Home Depot. She estimated she saved over a $1k.
Most professional roofing companies recommend a full tear-off. If you put the new one, over the old one, you might get a few less years wear out of the roof.