I want to install a 15-amp AC receptacle in my basement between the ceiling joists. The basement's not finished so there's plenty of room to play around. Should I be installing a "new work" new plastic outlet box or a steel one?
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.
With NM wire, I'd go new-work plastic myself, I find them easier to work with.
The metal boxes must be wired to the ground wire, and they need inserts for the knock-outs to keep the NM cable from possibly being cut by the sharp edges of the knock-out holes. With plastic, neither of these is a concern.
Also, remember that if you plan on finishing the ceiling, mount the box so it will be eventually flush with the drywall, not flush with the joists.
It's not related directly to your query, but don't forget to use a GFCI! It's required by NEC 2008 in an unfinished basement unless the outlet is dedicated to a security or fire alarm system. You may also want to go with a 20A to give you plenty of flexibility with how you're able to use it in the future (larger power tools, sump pump, etc.).
the best way to do any electrical project in your house safely and efficiently is to hire a licensed professional. if you are uncertain on how to do electrical work, no offense you should not do it. the national electrical code is extremely strict and local inspectors are cracking down on do-it yourselfers. please as a licensed electrician do not attempt if you have not the proper training, thank you