The backup rule of thumb is 321. 3 Copies, 2 Formats, 1 Off Site.
I've been burned, so I might backup more than you.
If important, I burn the out-of-the-camera files to optical disk, 2 copies. This is done before editing or sorting. If time and equipment permits, I print a contact sheet.
The computer gets a full back up about monthly. I use two different external drives in a rotation. This covers any edited output or work in progress. If there is a lot of work not backed up, I will back up sooner.
For an external drive, I get a bare drive and an enclosure separately, allowing either to be changed when the technology improves. Usually the second largest drive available is the best price point.
After editing, I might burn the files to optical again and file it with the disks created right out of the camera.
If your system croaks, you may not immediately get it back up. I have a number of USB sticks of different sizes. From time to time, I'll copy select photo folders and other often used files onto to these. This bag of sticks means I can use another computer to work with them.
Offsite can be family, or someone you make an arrangement where they have a filing cabinet at your place, and you at theirs.
3-2-1 might cover half your backup problem.
Over time, storage is replaced with new technology and it will become more difficult and expensive to get information off it. From time to time, bring files on older media forward. When you get a new computer is a good time to do this.
File formats need to be brought forward too. Adobe no longer supports older Pagemaker files in InDesign -- it went away one day. There are only a few programs you can use to read Kodak PCD disc files. Popular file formats of the past are unreadable now.
For [lossless] file format protection, DNG and TIFF might be the two formats to bet on. There is no way to predict where this will go.
Finally, no backup system is worth anything unless you test your restore process from time to time.