If you have enough free space, it should be on the system (startup) disk. That's the default.
Using an external drive as scratch disk is always a suboptimal solution. But if you're about to run out of space, you may have no choice. You need at least 50-100 GB, possibly more, depending on your file sizes and work habits.
Note that low disk space on the system drive is a potential concern in its own right, and regardless of Photoshop you should never let it fill up beyond 60-70%.