What is the highest rated HDMI category available?
The latest and greatest HDMI specification is 1.4a (and version 2 is expected to be released this year). The fastest/highest bandwidth category of HDMI cable is "HDMI with Ethernet." The rating of a cable's shielding (Class 2, Class 3) has more to do with fire resistance and US wiring code and is not really relevant to the matter of signal loss. MyCableMart.com has a great article with more information and cable recommendations: http://mycablemart.com/help/hdmi_which_one.php.

Whether a given cable available for purchase is higher quality with more more shielding is a matter of finding a good vendor and vetting their claims (caveat emptor). Longer cables with thicker wires inside, e.g., 22 AWG versus 24 AWG, will, all other things being equal have lower signal loss. 

However, my experience with long HDMI cables has been very hit and miss. Just this week during an install for a multicamera livestream, a brand new, 50ft HDMI cable with built-in "signal booster" would work when connected to a monitor but not when connected to the video switcher (a Blackmagic ATEM Television Studio). A Blackmagic technical support technician told me that TVs/monitors are engineered to be very forgiving of signals that have fallen off spec. The ATEM switcher is more strict (and rightly so) and would not display the signal. Furthermore, I was told by Blackmagic that after 10 feet, HDMI cables start to fall off spec. In the end, we purchased an HDMI to SDI converter and successfully got the signal from the computer to the switcher.

After this and other HDMI misadventures, my gut feeling is to avoid long HDMI runs in favor of SDI connections or CAT5 baluns/extenders. YMMV.