While the post above is, in most respects, accurate, there are a couple of things you need to be aware of.
First, yes, Snow Leopard, OS 10.6.8, is a very good OS. But, if you are using any third party applications, you need to insure that they are compatible with OS 10.6.8. Some third party apps have "advanced", in that they will not work with older versions of the Mac OS.
Secondly, be aware that there could be some apps that will be updated, and especially for Security Reasons, but that you will not be able to apply such updates, assuming they will no longer work with OS 10.6.8. In particular, that could be true of the Safari Browser. The version that comes with OS 10.6.8 should work fine, but any security concerns will, most likely, not be addressed by Apple with older versions of their software. The same thing could be true of other browsers, like Firefox, Google Chrome, and Opera.
Third, when you purchase Snow Leopard, it will be on a DVD. So, hopefully you have a DVD drive.
Fourth, there is the possibility that you could start with a newer OS, which could alleviate some of the compatibility/security issues I stated above. But, without knowing what exact Mac Model you have, it just might be better to go with OS 10.6.8.
Fifth, yes, SuperDuper! is great! However, be aware that the newest version, V2.9.1, is compatible with OS 10.8 and above (see, that's an example of what I stated above). However, V2.8 is compatible with OS 10.6.x. This link explains all that:
http://www.shirt-pocket.com/SuperDuper/SuperDuperDescription.html
Sixth, the step:
4) Copy your applications and files from the backup to the Macbook.
is not what will actually be done. After the installation of Snow Leopard (or whatever Mac OS) is done, you'll be offered the opportunity to "migrate"/copy all your needed "stuff" from the SuperDuper! backup. You need to choose that, and then all the needed "stuff" will be "copied" from that backup. You will not do the actual copying. In fact, don't just copy the stuff yourself. Let Migration Assistant do it for you.
Additionally, it is best if you get into the habit of making backups as often as "possible". I use SuperDuper!, and backup both of my Macs to two different external devices (one is a "standard" 1 TB HDD, the other is a 512 gig SSD) once a week. Also, make sure your external device is OK. You can use Disk Utility to check it out.