The Arduino Uno is the most common and easiest Arduino board.
If you combine Arduino Uno and a Ethernet shield, you can make a webserver.
The Arduino Ethernet is a single board that combines the Uno and the Ethernet shield.http://arduino.cc/en/Main/arduinoBoardUnohttp://arduino.cc/en/Main/ArduinoEthernetShieldhttp://arduino.cc/en/Main/ArduinoBoardEthernet
Using a W5100 based ethernet shield makes things easier.
The ENC28J60 based ethernet shield will work, but the library is not included with the Arduino.
I would suggest to buy an Arduino Uno and a Ethernet shield.
You can use the Arduino Uno to learn how to use it, and try a few examples. The examples are included in the Arduino IDE (the software).
If your sketch would get too large, you can replace the Arduino Uno with the Arduino Mega 2560.http://arduino.cc/en/Main/arduinoBoardMega2560
If you buy a clone from Ebay, they have cheap components and sometimes they have problems. The older version of the Arduino Uno and Arduino Mega boards work the older version of the Ethernet shield.
If you buy the newer R3 (or Revision 3) version, both the Arduino board and the Ethernet shield should be version R3.