What is a fast growing shade tree? One that doesn't grow too high? I'd like to plant 2 of them about 12 feet apart. Would let them overlap to provide canopy of shade for outdoor area.

Poplars, Weeping Willows, Sycamores, and varieties of Ash and Maple are fast growing!

Poplar trees usually grow fast, but tall. Most ornamental varities of trees do not get very tall. If ypu are looking for shade, you will want to avoid trees that drop things like nuts, sweet gum trees, etc. Also avoid those that have berries or the like that would attract wasps and/or birds. Red buds and dogwoods are usually a good choice.

They seem to have a lot of stuff and I would trust whenever they recommend

I think any good tree would work if you prun it well every year.

I'd call or stop by and talk to a specialist, plus then you can see.