Roger's Park is my first choice because more motorized watercraft dominate the waterways between Roger's Park and the bay. We typically leave a car there early in the day to shuttle drivers back to get their vehicles to load our equipment. If you rent, that's all taken care of for you. The county has provided great landing where you can take your craft off the water and load your vehicle. There is a swimming area where you will find people floating in the water. My daughter always enjoys Kona Ice while she waits for us to finish packing the car. You can even launch from this site as well as rent equipment, but there is nothing fun about paddling up river.
I would suggest, if you have the time, that you actually drive to the west coast of Florida. That area looks nothing like the coastal areas of most of Florida. If if you bring your own equipment, you do need to make a reservation to launch as the tiny launch site can get really crowded on the weekends. I prefer heading there during the weekdays in spring or summer. For Orlandians, just head west. After a day of paddling, I recommend a stop at Becky Jack's Food Shack.
How will you spend your wild and wondrous Saturday?