Your notebook should equip with DVD combo which can read/write CDR/W but read DVD only. DVD burning software will not get your DVD writing capability.
Option 2 should be using standard internal DVD-burners for PC, connecting with USB-to-IDE converter and power supply. This costs around $400 but it is not portable. And your notebook must support USB 2.0.
Option 3 is to buy a slim internal DVD burners. There is no retail product in HK, but you can go to notebook repair shops for quotation and installation (You cannot install it yourself). I have get quotation a month ago and it is around $800. (with installation service and a slim internal DVD multi burner) This is good for old notebook that supports USB 1.1 only.
External DVD burner may be cheaper and less hassle for DIY, but the portability of your notebook decrease because you have to bring the cables and transformers and need to plug in external power (some slim models may be bus-powered so no need to use transformers and external power supply but at a lower burning speed)
Replace the internal optical drive with slim DVD burner needs professional service, but once done you have no extra things to carry. The only thing you may worry is that it may not be reused when you change notebook. But if you change the notebook in near future, you should wait and buy a model with built in DVD burner!
In my opinion I will prefer change the existing optical drive with a DVD burner.