Cloud backup is awesome - it's just there, it works no matter if you're at home or on the road, it runs continuously in the background without you doing anything. Should you do cloud only? No. Will it cover you in a catastrophic event - yes(ish).
There is no harm in keeping old media around (cd's, dvd's, hard drives), but I would only consider them an option of last resort. Having your entire archive on a small number of current tech drives is highly recommended - managing a single(few) 14tb USB3 drives is easier than a stack of disc's or assortment of 1-2tb HDD's.
As to software, I'm mixed a lot of different ways. Backup software wants to write to custom backup files. You have to use the same software package to read those files & you have to restore them somewhere else to work on them. Some backup products will make incremental backups, then consolidate them into larger files, and rely on the entire chain of files to be good to do a restore. Hourly files get consolidated in to days, days consolidate into weeks, etc. Some times these consolidations fail, and you'll need to start a whole new backup, on a new backup drive.
Backup is great for your c: drive, or your internal storage on a Mac. Backup is good if your external drives are still small - say 4-5tb of data. Once you get over 8-10tb of data, you don't want to 'backup' those files, you want to 'sync' or 'archive in place' them. Products like Chronosync and GoodSync come to mind, but your needs may be different. Instead of writing them to a backup file, they stay in their normal folder structure. Then any 'changes' that are seen, the current file can either be overwritten, or archived separately so you can review them, or keep then.
It's all about the work flow - how you import photos, how you manage the cards that were just imported, etc.