Regardless of which new console you're looking at, storage is going to be a precious commodity. That goes doubly so for the PlayStation 5 at launch, as it won't support internal storage expansion right away and isn't going to let users backup their next-gen games on external hard drives. We do know that expandable storage is coming, though, and Sony's saying that it may also let users store PS5 games on external drives as well.
As spotted by Twitter user Wario64 in a massive PS5 FAQ published by Sony, the barrier to storing PS5 games on external USB drives may not be a permanent one. Just as with the Xbox Series X and Xbox Series S, Sony is requiring that all games designed for PS5 be installed to the console's internal storage, but at launch, you won't even be able to back up something like Miles Morales or Demon's Souls. That could change sooner rather than later: "Explorations for allowing players to store (but not play) PS5 games on a USB drive in a future update are underway."
Sony hasn't provided a time table on when such an update might ship. It's quite possible that we'll get the guaranteed update for expanding the 667 GB of available internal storage with approved M.2 drives first.
For PS4 games running in backward compatibility, those can both be stored on external USB drives and played from them. In theory, peak loading improvements aside, backward compatible PS4 games should still benefit from other performance boosts while running on PS5. If you want to play an older title that's being updated to PS5 standards, like No Man's Sky, it will still need to be on the internal storage to take advantage of the console's fast solid-state drive.
Until Sony starts publishing its list of approved M.2 drives, there's no reason to rush out and buy one in the hopes of expanding your PS5's internal storage. As for external USB drives, Sony advises using a drive with USB 3.0 speed or better, with anywhere between 250 GB minimum and 8 TB maximum of storage. "Devices with a faster specification may result in shorter load times for PS4 games stored on the drive," Sony says, so you'll probably want to look into USB 3.2 drives if you're going to buy a brand new one.