I'm looking for an external device to back up my files and applications on my iMac. I would like it to hold 250 or 500 GB and to be rather cheap. What is the best option, one that is simple to use (and maybe can use the Time Machine backup software)?

What is your budget? For not much more than 500GB you can get terabyte drives these days. I use the Mac friendly, plug it in and forget it, WD My Book 2TB. Which contains 2 hard discs of 1TB each. One is set as a general storage disc and the other as a Time Machine back up (backing up the iMac's disc and the other 1TB disc). The discs are swappable - should they fail just put another one in and the FireWire 800 connection gives speedy access.

Most brand name drives will be fine with the iMac. Some may need reformatting to get the best from them but that is not a big deal.

Cant you just buy an external hardrive? They sell 1 tb pretty cheap now