Weller WE1010 is a temperature-controlled soldering iron. It comes with a digital display that shows the current temperature of the iron. Weller WE1010 is a great soldering iron but it is more expensive than WLC100.
I hope that you have checked your headphones as well - the mating connector on your headphones could be damaged. If you have to replace the jack on your ipod, there is a useful guide about how to solder with a soldering iron at: http://soldering-irons.com/how-to-solder-wires-together-solid-stranded-3-two/
You can order de-soldering wick online at the websites of any major distributors of electronic or soldering components. I do a lot of shopping online at Digikey and I know that they have a wide selection of de-soldering wick in different sizes. Amazon.com has also a good selection of desoldering wick. You can remove solder by placing your wick over the solder and then heating desoldering wick with soldering iron. More details about how to use soldering wick is here: http://soldering-irons.com/how-to-solder/remove-without-pump/
Use one of temperature controlled soldering iron with a digital display such as the Weller WE1010 soldering iron. That way you will be able to precisely control the temperature of the iron to within 9 degrees Fahrenheit. There is a guide for choosing the best soldering iron: http://soldering-irons.com/best-soldering-iron/ Regards