What kind of battery to choose for my electrical car project
I want to drive the car on house with a decent speed. Not like that
  competition cars.


For similar performance to the stock setup you want a similar voltage. AA cells put out about 1.5v to 1.1V each depending on load and discharge state, so to replace a 6 cell AA battery you want something that delivers from 6.6V to 9V. It also needs enough capacity to run the Raspberry Pi (with any addons) as well as the motors, for a reasonable time.


  I saw that if you are not careful you can damage the battery if you
  discharge too much or overcharge.


That's true. Lipo batteries need to be charged with the right type of charger, and must not be allowed to over-discharge. Over-charging or charging a damaged Lipo may cause it to catch fire and burn up everything around it (including your house!). NiMH and Nicad have more relaxed requirements and are safer. 

The standard battery for RC cars is a 6 cell 7.2V NiMH or Nicad pack. Batteries for smaller cars typically use AA or 2/3A size cells. eg. ProTek RC 6-Cell 7.2V Speed Intellect NiMH Battery (1600mA 2/3A cells). If your car used individual AA cells in a holder then another option might be to use 6 AA size NiMH cells.

To run the Raspberry Pi from a higher voltage you need a regulator to drop the battery voltage down to 5V. In the RC car world this is called a 'BEC' (Battery Eliminator Circuit). A switching regulator or SBEC 'transforms' the voltage down through an inductor, so it can be very efficient and draw less current from the battery. Here's an example:- HobbyKing™ Micro BEC 2A/5v (Switch Mode).