What type of relay is proper to use for this motor driver application?
I now want to size a solid-state relay(safety relay) for the driver of a servo motor as illustrated below:


Solid state relays are generally not suitable for safety applications. Semiconductors can fail short circuit leaving your circuit energised and unsafe.

Your illustration concerns me. There is no indication that you understand circuit theory at all.


  Relay will activate when there is fault.


This is an unsafe practice. Safety circuits require the safety rated relay to be active when there is no fault. Failure of the relay should result in the circuit going into a safe mode (stopped in this case). In most industrial applications dual-redundancy circuits with fault monitoring are used. A single failure will still allow the safe de-energisation of the circuit and monitoring will prevent reset until the fault has been cleared.


  But since the load is inductive in this case i.e the load is a motor; 


The load appears to be a variable speed drive, not direct connection to a motor.


  Im worried if I use a electromagnetic relay or a random fire SSR there may occur inductive spikes during relay action(?). 


You need to study the inrush characteristics of the controller.


  Is it better to use a relay with zero-crossing relay for this kind of application?


Relays are mechanical and cannot provide zero-crossing capability. Solid-state relays provide zero-cross capability but are not suitable for safety applications.



You are out of your depth in this project and I recommend you get professional help, carry out a risk assessment, document the safety performance level required by the application and document its implementation.