You are correct. iCloud is not a backup solution, it is a syncing feature to keep certain files up to date across all your devices. For a complete backup you need an external drive with either Time Machine or a clone.
Any external drive will work. I prefer the Mercury Elite Pro line from OWC, a good source for all things Mac:
https://www.macsales.com
When you get the disk be sure to reformat it, Mac OS Extended (Journaled). That will remove any pre-installed software which is unnecessary for Mac.
I keep both a Time Machine backup and clones. You can use a cloning software like SuperDuper! or CarbonCopy Cloner.
The advantage of the clone is that you can boot from it and use the system. So, if your hard drive fails you can just boot from the backup and keep on working until you have the time to repair or replace the internal drive. You can also drag and drop files with the clone because it is the identical file structure on your primary drive.
The advantage of TM is that it creates recursive backups, so you can restore a file or the entire drive from a certain point in time.