It's good you want princess cut its 30% less than a round(the king diamond)
If your buying a nice stone like that you want it GIA certified and the serial number lazered in the stone,so when you have it cleaned you know your getting your stone back even though you will prob be able to tell it yours(the inclusions). There are other grading company's out there that are easier graders that jewelry stores will try and push on you. What ever the weaker graders grade is the stone in reality is a grade or 2 lower than what's on the paper. They do this to make you think your getting a higher graded stone for less,your really getting a lower quality stone with a generous report card
You want your stone graded excellent in polish,cut,and symmetry this is very important. Once these 3 are ALL rated excellent can you fairly compare color and clarity grades.
1st and IMHO the most important is the color. If you don't want to see yellow in the stone which I'm sure you don't the stone HAS to be D,E,or F. You Will see yellow if it's not a F or higher grade with the naked eye. Buy a smaller stone before you buy a larger yellow one. Obviously the higher the grade the better.
2nd is the clarity unless your paying 100k+ all stones will have a inclusion somewhere, the larger the inclusion the lower the score. Personally the lowest I would go here is a VS2 especially with the larger stone. The little ones you mite be able to get away with taking a lower score if they look good to the naked eye. Also try to get the inclusion on the side of the stone so you can cover it with one of the prongs that hold it to the ring
Good luck congrats
