60D manual says : 330MB/min = 5.5MB/sec for HD filming both in 720 and 1080 modes.
So technically, in your case for video, any SDHC card with more than 5.5MB/sec minimum write speed is overkill.
A fast card would save you a lot of time while transferring those huge videos to your PC so I would recommend getting one anyway. I would skip the fastest cards though, to save some cash to spend on a decent card reader, which will get you closer to the maximum speed of your card while transferring files.
Your card will be formatted as FAT32 for your camera to use it and this file format has a maximum file size (for a single file) of 4GB. This is why you need to stop filming after 12mins, because at a rate of 330MB/min, it would take 12mins to get to 4GB. Like others said, you can start filming again, this obviously creates a new video file, then you have another 12mins until the file size limit is reached again.