A standard Arduino board is now under $10. A W5100 Ethernet shield is also under $10. A LCD keypad display shield is under $6. Debugging Arduino can be done via the serial port, but for out in the field there are some advantages to having a display. Adding a display can be done in many ways, and for this project we are looking to use premade boards. There are two small catches - some pins clash with the Ethernet shield and the LCD shield, and also the display shield shorts out a few pins on the metal of the Ethernet plug, so it needs to be raised up higher.
To get a cheap board, search Arduino on ebay and sort on price+postage and “buy it now”. Then for the Ethernet board, search on Arduino Ethernet. For the display board, search Arduino LCD Keypad.