SDHC - This is the standard that allowed for larger sized SD cards (4 GB and up). Personally, I do not typically use a SDHC cards for two reasons. One, the standard cards are cheaper as you are not paying a premium for the higher capacity cards, and two, it worries me greatly to wind up having too many images on a single card, So I would rather have (and pay less for 2 - 2GB cards rather than paying up for a single 4GB card).
Class (2, 4 or 6) - marks the speed of the card. Usually seen on the higher capacity (SDHC) cards, it tells you how fast something can be written to the card. Since even Class 2 is fast enough to handle the writing speed of the G9, you don't need to pay up for the higher speed cards, because they will provide no benefit.
High-Speed - Not really all that important. And card for any reputable manufacturer (SanDisk, Lexar, Transcend, Kingston, etc) is going to be faster than the speed the camera can write to the card. Again no real benefit to paying up for a faster card that will have no bearing on the speed.
In short, stick with any top brand name and you will be fine. Don't worry about the "extras" as they will only be money spent on features that cannot be used with the camera.