A universal ROAD derailleur cable will work just fine; usually about $5.00 - $7.00 each, depending on where you purchase it. If the piece of outer cable housing next to the derailleur is in good condition, flush it out with some spray lube, put a little dab of grease on the end of the cable and thread it through the housing, then re-connect the cable to the derailleur. Make sure the shift lever is all the way down towards the ground, and the chain is in the smallest rear cog.

NOTE: IF you have to replace the outer gear housing, make sure to save the housing caps on the ends of the old housing; you'll need to put them on the new piece of housing. Those end caps are special to the frame set.