External drive

Literally anything you want

 

Anything. It's just like a regular hard drive, it just doesn't reside inside your computer.

You could even load OS X onto it and boot from it if you wanted/needed to.

A hard drive's a hard drive.

 

Install as you normally would, just point the installer to the external drive. In the case off apps that simply need a copy and paste into the applications folder, do the same thing, except copy to the drive instead of the applications folder.

Of course you can keep apps on both, why you'd want to is beyond me though.

I think you're trying to overthink things. Treat the drive the same as you would treat your "Macintosh HD". It's the exact same thing.