Hefe's build would serve you longer, but it does not include an optical drive.
For God's sake, do not buy an LG drive! I've got an LG doorstop sitting here beside me... worked for a couple of weeks and died. Their RMA policy is basically you don't get one because they will find something wrong with it and return it.
If you already have a computer, post the make and model of it. You should be able to reuse some of it. If the case will work that would save you some dosh right there, as well as the optical drive. A new hard drive may be the way to go, though.