@goodiventor.
If you have an Ethernet shield already, why not use this as the primary interface, just like your router at home.
Using JavaScript, you can leave all fancy stuff (graphs/tables/animation) to the client browser. And use simple ajax commands to communicate with the Arduino.
Another project you may be interested in, is turning your current setup into is a Graphic/Programmable calculator.
This does not need to be super fast.
You will need to build a stable parser for expressions.
The parser can slowly be extended to run programs (scripts).
And TFT's like the ones shown above are Arduino compatible.