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1) For the sensor you need to decide whether you need a 2D map of the environment or 3D. For 2D case you can opt for laser range finder (lidar) and in case you need a 3D map you can utilize kinect.
2) To start with mapping there is a lot of literature available. I would recommend you to start looking up theory for SLAM. Some of the links I found useful link text . Here you can find step by step progress of working with mapping module as mentioned by Saurav.
3) For completely autonomous robot you need to look at path planning stuff too. You can have a look at Computational Motion planning course at coursera for some insight.
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