Control Arduino From Phone

Hello everyone! I have an Arduino setup here to a motor that turns a knob 180 degrees for my heat on and off.

1) How can I control this from my Android phone via Bluetooth? 2) How can I control this from my Android phone while on the road via WiFi?

Any guidance would be appreciated, specifically a parts list needed to do each item.

Do I need a WiFi Shield? http://www.amazon.com/dp/B009M8BU50/ref=wl_it_dp_o_pd_S_ttl?_encoding=UTF8&colid=2F9MFCSO07L2N&coliid=IYI7IQEJC0N23

And a wireless transceiver? http://www.amazon.com/dp/B00E594ZX0/ref=wl_it_dp_o_pd_nS_ttl?_encoding=UTF8&colid=2F9MFCSO07L2N&coliid=INQ0UUT921DUU

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Bluetooth, You write an Android app that sends text commands via the bluetooth device on your phone to the bluetooth module connected to the Arduino

On the Arduino you write a program to interpret the text commands which you are sending, and use those commands to control the motor

On. Wifi you need to configure your wifi shield as a server

On Android you write an app which sends commands using http GET
At the Arduino end, you write code to parse the GET requests and used the information to control you motor.

Note. I think there are some apps that allow you to make buttons on Android and send commands based on those buttons, but you would need to pay for those apps and the may or may not do what you want.

Wow thank you for such a detailed response. So if I have my Arduino and motor working properly, what other hardware would I need to get? Are the WiFI shield and wireless transceiver that I linked sufficient for this project? Anything else?

Bluetooth HC05 or HC06 is your best bet, its cheaper and easier than Wifi But range is less than wifi

Wifi is much harder to use, and you'd have to decided if you wanted the wifi to act as a base station or another client etc Also wifi is a lot more expensive than bluetooth

All that being said I have a non bluetooth Android tablet and communicate to my Arduino using a Wifi to Serial module (but its not as easy as using bluetooth)

Thank you! One last favor... could you list out the hardware I would need to connect to my Arduino from outside the home through wifi? Essentially so i can be in my car and turn on or off my arduino using my cell phone.

Wifi shield running as a server? Wireless transceiver connected to arduino Some sort of hardware hooked up to my computer so I can connect to my home via IP address remotely? Would I need a static IP address at my home?