Ethernet is usually has a speed limit of 10mb per second, Fast Ethernet raises that to limit 100mbps, and gigabit raises it to 1000mbps. Most modern modems and routers usually come with Gigabit Ethernet interfaces, and that can be used in your own home. I would say that gigabit is the most common, but the other two still exist and are still used. Getting Gigabit devices are definitely the best bang for your buck, because in all honesty they aren't that much more expensive, but .
The obvious main advantages is quicker speeds, but speeds rely on different aspects. Most of us don't have fiber for our internet connections, so the majority of us likely have less than 100 mbps service. Another problem is that if you have a mix of gigabit and fast Ethernet devices, you are limited to the capabilities of the Fast Ethernet devices. Also, it is important to have atleast Cat5e or Cat 6 Ethernet cables to handle the higher speeds.