You have a major project in front of you. I'll try to give you some pointers.
First...yes the project is doable, but it's going to be complicated. Try to figure out what you really need or not...for example, does the lighting really need to be controlled via wifi or could you script it all?
You can definitely control EL strips with Arduino; here's a shield from SparkFun for it: http://www.sparkfun.com/products/9259
There's a million examples of controlling LEDs, so no need for more detail there.
As far as which board to use - that depends on how many things you want to control independently...if you need a ton then the Mega Is the way to go, but be warned that you'll probably have to do some manual soldering to get it to work with most Ethernet shields (they usually use SPI to communicate, which is on pins 10-13 of the regular board but 50-53 on the Mega).
Good luck with your project.