My suggestions:

*Any fast or rapid growing, clumping bamboo
*Paulownia Elongata, as for the rapid growth, large canopy, beautiful flowers, and ease of propagation by cuttings
*Gumbo limbo, as for it's nativeness to Florida, fast growth, large trunk, large canopy, and ease of propagation by cuttings
*Carrotwood for its medium-fast growth, large canopy, and ease of propagation by seed

To propagate gumbo limbo trees, all you need is a 3 foot branch and stick it in the ground, water it every 1-2 days, and watch it grow!

To propagate Paulownia Elongata, all you need is a cutting between buds where new leaves are about to appear, and stick it in a pot w/ potting soil inside, and watch it grow! This can also be done with large root cuttings.

To propagate bamboo, split at the rhizome(s).

If you are young, and plan to live in your house a long time, a live oak has that form. Red Bay also has it. That is, they eventually get a 30, 40 foot spread or more, with equal or greater height. In the meantime, maybe some trellises for vines??

Bill

Golden raintrees grow pretty fast and get pretty wide not to mention beautiful when flowering

Oh, I definitely am in the same camp as Bill. Nothing like a live oak for year round shade. Great for wildlife and they are native. They really don't take that long to get a decent size. Buy the largest size you can afford.

Make sure to research whatever tree you decide to get. You don't want to end up with another problem tree and have to start over.

Anna

Oh! Golden raintree,my favorite!
Tony has some seeds that he might share.
Felix

Golden raintrees are nice trees, but they only get to about 20-40 feet, that is an average of about 30 feet.

Check out the bottom of this link for the list of trees .
This article has excellent advice on tree care for newly planted trees too .
Check with your Extension Agency or Division of Forestry for your county .
Any chance there is a Master Gardener Plant sale coming up in your area ?

Here is a link that might be useful: Trees Suitable for Urban Areas in Florida

I'd be willing to wait for a quality tree...in fact I AM waiting. I pulled out a rather large (but not huge) camphor tree that was giving pretty decent shade but was very close to the house. I've replaced it with a live oak.
I believe that carrotwood trees are invasive and that gumbo limbo can't take too much cold so I'd be careful there. Like what has already been said: do your research.

Actually, Paulownia Elongata trees are good quality, and they are the fastest growing tree on Earth. The roots go deep into the ground in search for water, so less problems with the roots, but the roots still shouldn't be too close to a house. If you fertilize and water close the the tree, the roots will stay near there.

There are also many very good quality, fast growing, clumping bamboos, but they can get expensive. Look around and see what you want.

If I were you, I would get a fast to rapid growing tree that will grow tall, to get shade faster!