Kevziek,
You should be able to burn CDs with your computer, but I think you'll need to buy an external burner, a firewire PCI card and Toast in order to do it. What OS are you running?
I've had sketchy experiences with the compatibility of some add on PCI firewire, USB, video, SCSI cards in different models of Macs over the past seven years. Compatibilty can be hit or miss, and it'll be tougher with an older machine.
For burning CDs and DVDs I have had success with Macs of varying vintages.
I have a 1996 Powermac 8500 with processor and video accelerator cards, an internal Firewire/USB PCI card, and an external burner and Toast and it runs fine. I use a Dual 1.25GHz with a built-in SuperDrive at work which runs great. And I do all my iMovie and iDVD projects on a suped-up Apple Cube with an external LaCie SuperDrive which allows me to burn my Tivo content onto custom made DVDs.
It can be done with an older machine, but I think your idea of getting a $799 eMac is a much better solution. It comes with a built-in combo drive that will allow you to burn CD-Rs and view DVDs, so the only thing you might have to buy is a copy of Toast. Another thing you may have to worry about is getting used to using the new OS 10.3 Panther operating system.
Have fun!