Check out the START HERE Check out the START HERE robot. It is a great place to start. After that work on adding a few other things to build off of it. It is a lot easier to answer specific questions after you get started than trying to answer questions you aren’t sure to ask yet We’re here to help!
You could get Lego Mindstorms from ebay or try using a search tool like google, and type in "lego mindstorms" and your local asian word for sale or discount or delivery and see what that gets you.
You dont need anything except a computer to start programming it, all you need is in the box. A book with very easy to follow instructions and a CD with a very easy programming software.
If I understand your description correctly, you want a claw to pick up an object that comes within the claws reach. The Lego Mindstorms NXT kit has all you need for this. Motors, sensors, prosessor and enough construction material to build a funky arm and maybe even a moving platform to go with it.