Arduino Ethernet and Uno R3 as a firewall
As an entry level board, I wouldn't suggest trying this on the R3. You can do it to an extent on the Yun which comes with both a network port and wifi. 

Now that said, your internet speed will be severely hampered by the lack of resources on the yun. In which case, you might want to steer closer to the Intel Edison, which you can use with the arduino IDE. It is considerably more powerful.