How to determine the number of compression stages given a compression ratio?
You'll have to look up what the technology level can bring you these days. Usually, cycle design is s joint effort of what is needed and what can be done. Engine manufacturers have an aerodynamic department that is in close contact with the engine cylce designers and marketing.
An OPR (overall pressure ratio) of a design is based on the maximum turbine inlet temperature and depending on the cooling technology. Once selected, the aerodynamacists will tell you how many stages you're going to need. Since you're not a manufacturer, you'll need to choose a value, 1.2 : 1 is a value you can use. Note that a turbofan has a higher stage pressure ratio.