Holy hell, just buy something better. Don't waste your time polishing a turd. That thing is like a heated nail, not a soldering iron. The fact that it was sold as a "complete" solution, but didn't even come with a sponge--an essential to soldering--shows just how crap that thing is. I'm not being a electronics snob either. I've had that soldering iron before and it's a piece of shit.
You can get decent soldering irons for $10 at local electronic stores (NOT Radioshack), which feature actual soldering tips. Weller is a good brand, but basic soldering irons, with REAL tips can be generic brands and be good. Just don't settle for the garbage Radiodump panders to unsuspecting hobbiests.
Stands will run you $7 or something; I've seen them at Amazon.com for that price. Get a spring stand so you can just toss the iron in there without worrying about knocking it off. They also have a spot for the sponge, which is really useful--no, essential. A clean tip is very important for good soldering, and enables you to blob solder on the tip of your soldering iron so it doesn't oxidize and stop melting solder (like your heated nail suffered). Then you can leave it alone on the stand while you do other things without worrying that your soldering iron is dying. Wipe it off on the sponge and you're ready to go.