There is a simple way to back up small sites: get the web files and the database/s and you're done.
1. Get a good FTP app like FileZilla or Core FTP Lite. Then download every file and folder in the webroot. This is the folder (or directory to be precise) one level below the root directory. The webroot directory is normally called public_html, or http_docs, or var/www/html. It's the location of all web files. Get these and you've got the site.
2. Dump the database and get that, via phpMyAdmin thru cPanel (if you are using a DB-driven webapp like a CMS, blog, ecommerce etc).
If you've got the web files and the DB, you've got the site. There are some odds 'n sods like logs or whatever but none of those are critical.
The main difference is if you are using a dynamic app (one that runs off a database) or not. Either way you don't need any backup software, just FTP, unless you want to get complex or your webapp has an integral backup facility (as many CMS do). Another way to get the web files is to use Dreamweaver, for a plain HTML website, as that has an excellent sync & link facility that creates a local copy of the site. Even old versions of DW are good for this.
What you can do after that is to check that your backups are OK. This is the perennial problem because you don't know if they work until you load them up again and they either work or fail.
So to avoid tears at bedtime, install XAMPP on a spare PC. It's a LAN server setup that will run websites locally, even CMS and ecommerce. If you google 'xampp manual' you will find a most excellent website at Google #1 that will assist you in this regard
Then you can run all your websites on a local PC and test them out, including backups.
If you are using a CMS like Joomla or micro-cms like WordPress, you can get plugins that create a one-click backup of all files + DB. That's the modern way, no messing about.