SD vs SDHC vs SDXC has only to do with capacity with respective maximums of 2 GB, 32 GB and 2 TB. This impacts the file-system used on those cards (FAT, FAT32 and exFAT, respecitvely) and which devices are compatible with them.
Performance is governed by the transfer rate of each card. These are either represented by MB/s or by class. For performance of the camera, you are interested in one with a high write-speed, so pay attention to those who only quote a single number.
Memory cards now reach 100 MegaBytesmegabytes/s which is probably more than you need. Full HD video from the 60D requires 6MB/s so you will be quite safe with 15MB/s or more. If you shoot continuously in RAW, then go for something even faster.