I'm sure you'll have plenty of room for creating a tropical paradise, Susan. Don't despair. There are so many wonderful plants you can try out here, I'm sure you're going to have a ball.
Palm trees are easy care, don't take up much room and do give a pretty effect but, as Pam said, they don't offer much in the way of shade. You'll thank your builder for planting that oak tree in years to come for the cooling and shade it gives your yard. You can limb it up as it gets taller so it won't impede your view of the lake.
If you already have a gator, you can call and have it removed by wildlife control. That's a normal part of life here. It's also the reason many people have screened patios and cages around their swimming pools. Critters and bugs - there's just SO much more life here all year round than up north and you do have to get used to it.
