The most common cycad is called a sago palm. Of course, a sago palm isn't a palm at all, it's a cycad. And if you can't see the difference, it's understandable. Physically these plants are very similar to small palm trees, or even ferns.
Here in the Phoenix area I see a lot of sago palms. They are available at any Home Depot, and can do well in the right conditions. Unfortunately, the right conditions include protection from sun, and frost. When they're planted in the correct place, they look great. Out in full sun, they usually look kind'a sad. And their tips get burnt by frost.
Over the years I've lived here I've planted a lot of cycads, including sago palms. In spite of care, the sago palms have pretty much all failed, but the other cycads are doing great. Especially this one above, which gets a lot of sun, and was totally unaffected by the recent cold snap. It's called a dioon edule. Now, waitaminute, before you get all excited, it isn't one of those rare ones that are in collections, worth the big bucks. It's more expensive than a palm tree, but that's mostly because cycads are miniature plants that grow very slowly.
Personally, I like to snoop around garden centers when I visit friends in L.A. Here in the Phoenix area, there are people who grow them, and sell them, but not much.
Cycads grow for hundreds of years, so buy the biggest one that you can afford. The one in the photo in my garden I've had for over fifteen years, and it still looks more like a fern than a palm tree. By the time the trunk really starts to show, I may need some help trimming it, as it will probably be another 50-100 years. I'll probably be slowing down by then!