I second Orlando Vic's recommendation. From the airport, all the signs will point you toward Disney (& Universal) DON'T GO THAT WAY. Follow the signs to the other exit. It will lead you to S.R 528 (the Beachline). You want to take it West to I-4 toward Tampa.

You will hit 2 tolls - one immediately after entering the roadway, and it is for $1. The second is not that far away and is $1.25.

FWIW - for some reason I always get confused leaving the airport. I think after about 10 years, I finally got it straight. My clue that I went the wrong way was if I did NOT hit the toll plaza almost immediately If you do that, it's easy to turn around

To answer your question - if there is a non-toll road, well, I haven't found it, and it is going to take you a lot longer.