In the idealized analysis of the suitability of a particular thermodynamic cycle (Brayton, Otto, Stirling, etc.) for a particular application, the overall process is straightforward, and consists of several steps. In practice, though, the process is simpler than this; I'll describe both paths.
First, the designer determines what the hot source and cold sink temperatures will be. This will vary, depending on whether the cycle is to be driven by a combustion process, a geothermal source, etc., and whether the process is closed or open. The Carnot cycle is then invoked, so as to conveniently furnish an upper bound on the efficiency of the overall process, independent of the process details.
Second, the designer then takes the desired power output specification for the application (for example, the megawatt (thermal) rating of the power plant) and divides this number by the efficiency upper bound. This establishes a lower bound for the heat input rate of the process, and permits the designer to estimate the lower bound of the overall size of the heat input, work extraction, and heat rejection processes needed to support the desired power rating.
Third, the designer then looks at the characteristic process scale (set by step 2) and estimates for each possible thermodynamic process the practicality of each i.e., whether or not a (for example) Stirling cycle can be applied.
In practice, however, this is not how it's done. If the designer knows that the plant will be of megawatt scale and running on coal as the heat source, then (s)he also knows that the coal will be used to boil water into steam and drive an expansion process using a turbine, which then establishes all the rest of the big-picture design criteria for the plant.
If the plant is to be driven by natural gas and has a power rating in the tens-of-kilowatts range, then the designer knows to choose an otto-cycle prime mover, which again establishes all the big-picture plant requirements; if it's in the megawatt range, then the answer is a water-injection natural gas boiler on an open cycle, and so forth.
Or, if the required output of the plant is the generation of propulsive thrust instead of shaft horsepower and weight is to be minimized, then the right answer is a brayton cycle running on kerosene.
To summarize: The design criteria that are handed to the design engineer will almost always dictate which thermodynamic cycle (s)he will have to specify, based on knowledge of the current state-of-the-art and common practice.