Kell, UHS stands for Ultra High Speed (whatever that means).
Eye-Fi (not eye-if) allows the memory card to communicate via Wi-Fi to your computer (look Ma, no cords!) - you just have to do the set up on the card (IP address to your Wi-Fi) and boom - you can read your card from your computer like it is another computer on your network. Actually it looks like the card will just transmit the files to your computer if it is in range (after you set the card up).
Click the link you posted, and look at the image of the card. On the front of the card it says 64gb. Right above the 6 is a number 10 with a letter C around it. That tells you what speed class the card is. 10 is the highest class you can get now. That is what you want to look for in any card you get.
There is information about the speed classes in the second link hcmcdole posted.
Woe is me. The story of my life! CONFUSION! I went to get the Canon Powershot S100, their latest best mini. But when I saw it in person it was almost too small for me. And next to it was the G12. And that was actually not big at all, a bit bigger then my S90 that I just lost, but not too much bigger. So I had to come home and read about that one. But it is an OLDER model, out in 1/2011. I am not paying $500 for one that will be obsolete soon. It may be now.
I wonder where you can find what Canon's plans are for new models coming out. I love the Sony site, they have all the new models expected to come out in 2012 listed so you can plan!
I have no clue if they are about to come out with the next in the G series or if the newer PowerShot G1 X that came out in !/2012 is the improved model to the G12. But now we are up to $800 and heavier still. I still use my Canon T2i so am not sure if the PowerShot G1 X is too close to that one to use much.