The first thing you need to do, is determine if you want an external or internal drive.
An internal drive will cost you less and it'll also nicely fit inside your existing case (assuming you have room).
For an internal drive, you'll need an available 5.25" drive bay. You'll also need to determine if you have a SATA port, or PATA/IDE port available.
Preferably you'll want to go with the SATA option if you have a port available.
As for the drive itself, Pioneer, Sony, LG and Samsung are good options. Just make sure the drive you are buying has lightscribe support.
Any new drive you purchase now that is a DVD burner will support DVD-R, DVD+R, the various CD formats and double layer DVDs.
You'll also have to decide (if you buy an internal drive) whether to buy retail or OEM. If you buy OEM, you can save money, but it won't come with a cable or software (except in some cases they do still provide software).
For an external drive, you just need an available USB port. Plug it in and find a place for it to sit and you're pretty much done.
I currently have LG and Sony DVD drives both with lightscribe support.
If you give us your computer's specific model, I'm sure myself, or someone else can look up the details for you and what options are available to you.
That is, if you don't know yourself what options you have available to you.