Need more info? OK, normally you'd want a "High Speed" cable simply because they don't cost much more than a standard cable. If your device has Ethernet built into its HDMI connection, then you should get a "high speed cable with Ethernet". Simple right? Need to do a long length? That's when you need either an Active and/or heavier gauge cable. For a cable longer than 10 feet we recommend getting some kind of "active" Amplified/Equalized cable, and we like the Redmere chipset cables.
So why would you NOT use an amplified or Equalized (Active) cable? Three reasons. Cost, compatibility and power requirements. Active cables have chips in them and therefore are more like attaching a device than attaching a cable. The chip draws power from the Device with the Output signal. If the Device cannot supply enough current to run the chip then the cable WILL NOT WORK. Since its an electronic device it also may have compatibility issues such as handshaking problems or signal incompatibilities. In cases where the Source device is suspected of not having enough power to drive the Active chipset, then a heavy gauge cable should be used instead. Heavy gauge cables, such as 24AWG, are going to be heavy and inflexible. But if you cannot use an amplified or equalized cable and need a cable over 10 feet long a heavier gauge cable is going to be necessary, especially for higher resolutions like 1080p.
Still need more info? HDMI Cables & Connector Types What's a TMDS and why is it in my HDMI?