Backing up my files

About 10 years ago I had a tape drive to backup my files. It was very slow and didn’t fit in my later computers. I once tried to backup my files on cd’s but the number of cd’s I needed increased. On my iMac I was finally able to backup on DVD but now even my photo collection doesn’t fit on one regular DVD anymore. Should I buy an external HD and use Time Machine? If I accidentally delete some files, I can restore them easily. But wait, what if both my computer and the drive get lost or burnt? Today I discovered Mozy which seems to be the solution I was looking for. My files are backed up online so even if my whole computer gets lost, I still can reach my data.