Am I a dreamer ?
Lets step back. What is it you are trying to do? What part do you want to run on the Arduino and why? Is it where you are querying a remote database for a particular slice of the data? Or do you have some sort of physical sensors that you want to wake up every so often, record the current values, and ship them off to the database. Note that due to the speed of the Arduino and memory constraints, you will be limited to a small screen.
I suspect what you want to do is not do mysql on the Arduino itself, but instead talk to a custom client on the server (or a secondary pc) that you can send or receive the information you want on the Arduino, and the custom client does all of the interfacing to mysql.
If you just want a cheap system to do mysql, get a used PC and monitor from goodwill or similar recycling centers.