I happen to be very opinionated on the subject of shortbread.
My father always made it, and he swore that you could only make it in winter, when the kitchen was cold, or else you ran the risk of having soft butter, which is the curse of every shortbread maker.
He also swore that he could taste the differences in store-bought butter from one season to the next--for shortbread, he would only use butter from cows fed on Canadian red wheat during the winter.
He had similar feelings about flour--hard Canadian winter red wheat flour is the best.
He wasn't picky about the sugar, oddly.
He was adamant about the totality of ingredients, though: proper shortbread has nothing in it other than flour, butter, and sugar. Any recipe varying from that might yield a tasty product, but it certainly isn't shortbread. You can foul it up with vanilla or chocolate or nuts or whatever, and can call it snickerdoodles or s'mores or bimsquaddle or dingbat chow, for all I care, but you have no business calling it shortbread. Go nuts! Go crazy! Live it up! Just don't call it shortbread.
The proportions are:
1/2 pound butter
2/3 c sugar
2 c flour
If you can't, for whatever reason, marshal together the best ingredients, don't even bother attempting to make shortbread. You're not fooling anyone, you know.
Certain Scottish bakers--Scotland being the home of shortbread, after all--call for the addition of rice flour, giving the final product a nifty crunch, but I have not found that North American wheat flour requires such a supplement.
Some Scottish recipes call for castor sugar as well, but again--don't panic. "Castor sugar" in Scotland is just what we yanks know as superfine sugar.
Be brave, and proceed.
I am entrusting you with my father's shortbread recipe, which is an enormous responsibility, and I don't expect anyone to take it lightly.