Area ratio and the exit mach number 

For nozzle and diffuser, first you need to calculate Mach number and other flow parameter requirement.

I thing MACH NUMBER is chief factor to consider and pressure drop

Conservation of mass, momentum and MACH number...these equation will help u design the nozzle and diffuser.

KIndly note for which application ur designing 

The nozzle (accelerating flow) is not critical as long as you have a contoured profile.

Very critical instead is the diffuser design which depends also on the Reynolds number. You can find data on wind tunnels books. . However, a practical rule of thumb for axisymmetric channel is to have a divergence angle not exciding 6 degrees.

Regards

I forgot to say that what I said is for subsonic regime at the nozzle end. For supersonic, you could use the method of characteristic.

Area ratio, opening angle, Mach number, a little bit Reynolds number. Look to the Idelchik book of hydraulic losses. This book provides many helpfull information.

The nozzle either convergent nozzle for subsonic flow or convergent-divergent nozzle for supersonic flow

please read  compressible fluid flow by b.w.imrie

The geometry criteria such as: area ratio, cross sectional shape square or circular, round or sharp edges, micro or Macro, throat size, ...

The working criteria such as: back pressure, stagnation pressure, Reynolds number, ...

and the fluid  properties criteria such as: gas flow, ionized gas, plasma, liquid flow, gas mixtures, ....

I think the use of the nozzle/diffuser is the more important criteria you need to know, because, depending on the question's answer of "what is the purpose of the nozzle/diffuser? ", you can define what is the most important parameter in your specific case.

In some uses, you have only limited length, size,...etc. then you are not able to use the designed length, size,..etc.

Generally, for nozzles, the required exit Mach number is restricting throat, exit diameters, and nozzle length.  Via Method of Characteristic, you can design the supersonic part which has a great influence on the nozzle performance.

For the diffuser, the pressure loss is the most important parameter.

Regard.

Check this book for more info.

John David Anderson-Computational fluid dynamics_ the basics with applications-McGraw-Hill (1995)

Length available for the device.

The desired velocity change across the device.

Yes, All of theese parametersa are important.

Mach Number and flow rate