Generally speaking, disk space is cheaper than time: a 20GB hard drive would be plenty to handle your indicated image requirements, and you can get another one if you really need more; but there are only so many seconds in an minute (61 at most), and if they turn out not to be enough you'll be needing to speed your machine up or get a faster one. (I suspect that generating 15 thumbnails on the fly might involve a noticeable performance hit.)
Think of storing the smaller images as a cache. The script that displays an image first looks to see if the file has already been created. If it is, use it. If not, create it, use it, and save it for next time. Then only the images that are actually used are generated. If the original image changes, just delete the main/thumbnail images. You're also free to delete the smaller images ad lib if you like.
