***In arduino what is the best arduino to use.. maybe ur best choice..
The one that has the required number of input and output pins.
***In stepper motors(bi-polar and unipolar) when it comes to torque and accuracy what best motor to use or ur best choice.. Btw i prefer bipolar here..
The one that has the required torque and accuracy. Since you haven't said anything about what your torque and accuracy requirements are, you can't expect us to know.
***In the motor driver for the stepper motor what is the best to us that doesn't heat up fast.. ur best choice..
The best one to use is one that has the voltage and current capabilities, with plenty of reserve, to drive your motor(s). Since you haven't told us what those voltage and current requirements are, you can't expect us to know.
***What would be the best ethernet shield to use to put in arduino so i can have both the motor driver and ethernet shield plugged on my arduino?..
The ethernet shields are SPI devices, meaning that they use pins 11, 12, and 13 for communication, and typically use 10 for the ethernet slave select pin and 4 for the SD slave select pin.
The Wiznet based ethernet shields have more hardware supplied capabilities, offloading a lot of programming from the Arduino. As a result, they are simpler to use.
Since you intend to use shields, the answer to your first question needs to be revised to rule out any non-shield compatible variations.
By the way, there was not a programming question asked here, so this is the wrong forum.