Lighting control(Arduino-Android)

Well, i understand that making whole project without wire is too hard for a beginner like me. I searched a bit more and i found this video =>'Arduino controlling AC lamp with SSR - YouTube' That guy made a project. I think i can make project like that. He is also using an IP to connect with system. But the first diffrence his project and mine is = At the end of the video he controlled lights also with his iPad. But in my project i want to control with my android application. It will be simple application. When i run the application, application wants to connect internet. And i will reach the IP which i gave it. Then i will control lights.(But i dont know in this part do i need an android development kit for my arduino?).
The second diffrence as i said is my lights need to control other cities which are closer my city.
I dont have to use Arduino Mega ADK. I thought, my project will has android application for control. Thats why i said that. Equipments were my thoughts. We can change them. Cheaper way will be best for me. So, according to that video and my requests, am I gonna need 1 arduino, 1 ethernet shield, 1 solid state relay? But arduino and ethernet shields have a lot of types. I dont know which ones are best for me?