External Desktop or Portable for back ups? HDD or SDD?

I have a Sandisk extreme portable SSD which so far has been fab! It’s really quick for time machine backups of my MacBook Pro. For me the speed is quite important as I have a laptop, therefore I connect the drive, do the backup and put it away again.

In your instance, it sounds like you could leave the drive connected for long periods therefore speed may not be such a such consideration. That said…
If this is your only back up: I’d advise against leaving it permanently attached to the computer. If someone breaks in & steals the computer with the backup drive connected then everything is gone. If your backup is hidden away somewhere then chances are you’ll still have that. That does increase the overhead of having to fetch disk, plug in, back up, unplug and hide it again. Ideally you also need an offsite back up be that cloud or having 2 disks and rotating them on a schedule.

As for reliability, as has been mentioned by others, there’s no one answer, some people swear by WD and have had nothing but problems with Seagate. For me it’s been the reverse, I have a Seagate drive for backing up a NAS, that’s been brilliant however a WD drive has been the only one I’ve had to fail on me. Again, the only thing you can do to mitigate the risk is have multiple backups across various platforms.