Sarasota has its own airport. Its a nice small airport and easy to get in and out of, however since its small flying into it may be quite expensive.
Info on the airport is:
A cheaper alternative may be to fly into Tampa - the airport code for Tampa is TIA. Flying into this airport may save you up to $200 per ticket
I used to work as a rental car agent in Sarasota and I cannot tell you how many car accidents are caused by the sheer insanity of US 41.
First of all, this is a road with, like, eight different names: US 41, Tamiami Trail, Gulfstream Blvd, etc. It's crazy. Randomly, (or seemingly so to tourists) the signs change from one to the next, but end up again as either Tamiami Trail or US 41 (the two main names).
Also, a lot of people are thrown by the fact that this perfectly straight road suddenly curves and merges with 301, the other major road in Sarasota.
My advice is take your time in planning where you are going and look at the map carefully. The congested, old-folk-filled highway is not the place to browse the map.
In general the best way to get around is the car. But the public transportation system is quit got also. It gets you very conveniently to all important places. The downtown area is not so big that you couldn't walk through it.
Sarasota is best reached by flying into Tampa International Airport and renting a car for the one hour drive. There is Sarasota-Bradenton International Airport in Sarasota but the flights that come in there are very expensive.
The best way to get around Sarasota is by car.