I'm new to arduino, and I want to design a Simple Delivery Robot for Data Center, which has an arm to move items, and it follows line while moving.
I have no idea if there is a special arduino board for these types of robot or I can buy any arduino board.
My advice would be to buy a Uno and experiment with it on a small scale before committing to a larger project. Even the Uno can probably do what you want but you have not been very specific, probably because you don't know what is involved yet, hence the need to experiment.
How many motors and of what type ?
Where will the power come from ?
What kind and how many sensors are needed ?
What is going to move the arm ?
How many degrees of freedom will the arm need to have and what will power it ?
Will the arm have sensors on it or will it rely on absolute positioning ?
What is the weight and size of the items to be moved ?
How far will the robot move in say 8 hours ?
etc
etc
If you are new to Arduino, you are well off with an Arduino Uno Starter Kit for becoming familiar with sensors, actors and coding in general. This development system will be usable also with your further projects.
Then get the required sensors, motors and motor drivers for your device, and study the examples coming with these components and libraries. Once you could make it work in general, using a breadboard or shields, you'll know the controller requirements, i.e. mostly the number of I/O pins, whether USB or some remote control is required etc. Then you can chose a Pro Mini, Micro or Nano board, or build your own PCB.
The choice of the controller board will be a minor decision, all boards offer about the same computing power. More important is the choice of a suitably sized and stable robot base and arm, and the battery pack for the intended up time between reloading the batteries. You'll find several DIY robot kits in the web, often including a controller and basic software, or you can build your own mechanism.
There is nothing simple about that project.
What projects have you already done?