Rubik's - solving robot, what should I do?

Hi, 

I want to do a school project about building a Rubik's cube Solving robot. My idea of what I want to do is something like this: 

https://www.robotshop.com/letsmakerobots/node/31879

My questions are: Which is the best way to do it? Which components do I need to buy? How much would that be and, whould there be any cheaper options? 

I also want to state that I have never built a robot , and what I have to do the project is a 150$ budget, a windows computer, and about 6 moths.

 

Thanks, and sorry If something of what i've said is obvious/unnecessary. 

https://www.youtube.com/watch?v=ThMd9YR1MAg

Well , I have some knoledge
Well , I have some knoledge about rubiks cubes (I usually solve it in about 10 seconds) , but i can see why this is a bit too complicated. Should I start off buying an arduino board and some servos? Whare can I get those? Thanks.