Which outlet box should I use for an unfinished basement?
Unless you're using armored (BX, or metal-sheathed) wire, you can use either type box, your preference really. If you use BX, you need to use a metal junction box. 

There's a couple different types of boxes. The plastic ones with nails on them, and the metal ones with clips are designed to mount with their face 1/2" farther out than the front, which facilitates having them flush with 1/2" drywall when you finish it. 

There's also a type of metal box that's more rounded, with several knock-outs in it (and many types of equivalent plastic boxes) which are not designed for going behind drywall, and look a bit better when you actually do see them (if you care). 

Even if it's unfinished, you still need to put a cover plate on. The metal cover plates fit nicely over the rounded metal junction boxes, which makes them much less likely to crack if you hit them accidentally. Regular plastic covers can crack easily because they extend a far ways beyond the edge of the box.

It really comes down to personal preference on metal vs plastic, and then a question of if you will be drywalling, and intend this outlet to be available through the drywall. Also note, it's illegal to cover a junction with drywall: all boxes must be accessible. If you do put drywall up, you either have to remove this box, or have an outlet or blank faceplate on your ceiling.