Definitely consider at least going to 64MB of RAM. I used to have a system similar to yours with an old HP 8110e 4x cd-writer. They worked well together. However, if you're looking to get the latest and fastest cd burner, reconsider. Unless you upgrade your system, you won't meet many of the hardware requirements.
Newer burners usually require the following as bare minimum:
- Pentium MMX 200MHz
- 64MB of RAM
* I took the above from the minimum requirements for the PlexWriter 16x/10x/40x
Conclusion: If you don't want to upgrade your system just yet, then consider buying a used 4x or 8x burner on EBAY and save some money. 4x is the probably the highest transfer rate you'll achieve on your system the way it is...