iterate through values in an array of strings to print
I think this is the correct way to create an array of C strings:

    char * hvacSystems[] = {"Off", "Fan", "Cool", "Heat"};
    int activeSystem = 0;  
    char * displayActiveSystem = hvacSystems[activeSystem]; 

    if(systemNeedsToBeCycled){
        activeSystem++;    // make sure to set a bound for this variable
        displayActiveSystem = hvacSystems[activeSystem]; 
        tft.print(displayActiveSystem);
    }


Since strings are basically stored as char pointers so an array of strings is an array of char * variables. Or you could create an array of Arduino strings:

    String hvacSystems[] = {"Off", "Fan", "Cool", "Heat"};
    int activeSystem = 0;  
    String displayActiveSystem = hvacSystems[activeSystem]; 

    if(systemNeedsToBeCycled){
        activeSystem++;    // make sure to set a bound for this variable
        displayActiveSystem = hvacSystems[activeSystem]; 
        tft.print(displayActiveSystem);
    }