I got a new MacBook, I'm afraid of my data all lose one day, but I don't want to buy a giant hard drive and use time machine to back up my OS X.
If you care about the data then you need to design a system that implements there rules
(1) At all times the data must be store on three different physical media. Even durring a backup opearation, so if your backup software first cleans off the disk, yuo need four copies, if yor software is incremental, then three will do
(2) At all times the data must be store in two geographical locations. So you could rotate one backup drive to (say) your office. But you must plan this so all the dat is not in the same location, even for a short time. You may need four copies to make this work.
Yes, you can go cheap and skip some of this but if you want a file or a photograph to last 50 years the above is the MINIMUM. Over them long of a period simple schemes like Time Machine will fail
Think about all the ways to loose data. The major cause is theft or loss of the equipment, Fires, spilled liquid, teft andf so on. So keep the data in at least two buildings
Hard disks are a very good staorage media. Today you can buy a 1TB disjk for under $100. So buy three. What's good about disk is you know when they fail. When you rotat the backup drive in and can't use it you know right away. If you wrote your backups to DVD what are the change you would test the DVDs periodically to see if they still work? About zero. But a disk drive, you WILL test when it comes time for the next backup.
Periodic testing is critical. backups are worthless if you can't read them and you can't know if you can read them unless you periodically read them.
My guess is that inn 100 years there will be no 100 year old photographs, except those printed to paper.
Very few people bother to do backups, except maybe just use Time Machine