Thanks for the link Evan! We have a River Birch at our other house that is on the market, and have decided that we need one here. Like you said, they aren't really shade trees, but they do a great job of providing shade after the sun goes behind them. I really love that tree, and it grew very fast! We'll add some Aspens too. They aren't really shade trees, where you can sit under them, but they'll provide afternoon shade, which is what we need here. They spread bad, but I've got plenty of room for that.
I've been paying more attention to the trees in our area. There are a lot of Birch trees growing here, so at least I know they do well. Our neighbor has part of of property lined by them, and the ones that she has are huge, and do provide way more shade underneath than our River Birch was capable of. Not sure of the variety yet, but we'll get that figured out eventually. I have one on the east side of our house too. It's not nearly as tall as the neighbors tree, but it may be a lot younger.