Hi warsch,
Unfortunately the old Catch 22 kicks in here. In order to "adjust for grippier tires" you need to have "adjustable" suspension! If you don't have fully adjustable dampers (at least), your unlikely to release the full potential of "grippier tires"!
Given you intend to develop a "track dedicated Alfa Romeo 156 2.0 Twin Spark", a degree of suspension adjustment will be needed if you want to effectively realise the full potential of the car, its suspension, its tires and the driver!
I'd certainly install the stiffer rear springs, install a budget datalogger / laptime recorder, beg borrow or steal a quality tyre pressure and temperature gauge (the Alfano T36 is my choice) then play around with tyre temps and pressures.