Scratch

Rae writes,

I was considering buying an external hard drive to use for the scratch disk in Photoshop. They are very cheap right now. Does that make sense? Will it make things go faster?

Scratch disks are an important part of the Photoshop process. When you run out of RAM, it's scratch disk to the rescue. By default, your primary scratch drive is the same drive that your OS is running on.

Choose Edit > Preferences > Plug-ins and Scratch Disks...
By default,  Startup is selected in the First: dropdown menu.
Choose a second, third and even a fourth scratch disk drive.
Click OK.

Whatever drive you designate, it should be the fastest drive on your computer. Rather than using an external drive, consider installing a second internal hard drive or partitioning a section of your current drive instead. De-fragment often.

For best performance, Adobe recommends...
Scratch disks should be set up on a different drive than any large Photoshop files you may be working on. 
Scratch disks should be set up on a different drive than virtual memory.