there is no best controller specifically.it varies system to system.it depends on,

1.how correctly u did the modeling of the system

2.linearity and non linearity of the system

3.knowledge of the state variable and disturbances....and many more

literature review is the best thing u can do for the selection of the controller of your system

in general the controller is chosen by allowing the system requirements. One controller which gives better performance for one process may not give the same performance to other processes. Best controller means that it should give a balanced performance and robustness even uncertainties present in the system.

The best controller should be the one which is the easiest and simplest  to design and provides a desired performance/robustness for a given system of interest. It could be a PID (most common one) or some other types of controllers, e.g., LQG/LQR. In most cases, PID control would do a good job.

Yes the PID is the most one used in industry because of its simple calibration. However, when working in the research field, the easiest one is not necessary the perfect one.

So, in order to get the best behavior, do we need to to synthesis some controllers and choose between them to see which one is the more promising?

Every controller can be the best for your control system. It is about your desired behavior from the controlled system. You can choose the desired response according to transient response parameters, stability parameters like phase margin etc.  

the answer lies in asking the right question. What is the plant that you control? What are your controller's requirements?

Fractional Order PID controllers introduce two additional parameters corresponding to the order (possibly fractional) of the integration and order of differentiation. Speaking in broad generalizations, these additional parameters provide additional 'tuning constants' relative to standard PID controllers, and therefore the possibility for improved control performance for the same situations.

The catch, however, is that the one must build a working realization of a fractional PID controller.  Of the literature that I've read, this generally involves approximation by higher order linear filters.  Thus comparing FO-PID to standard PID devices seems is artificial. The more appropriate comparison is to linear systems implemented with standard auxiliary features including anti-reset windup and bumpless transfer.  In that case, I don't see particular value to introducing fractional order systems

As Francois said: Without requirements, any linear feedback controller is in fact the same as it satisfies the Bode Integral Theorem, i.e. some disturbances are rejected, some are gained, some signals are well tracked, some no ...