Brian Monetti, i <3 crafts
It is hard to tell (maybe 12x12 inches?), but what is important is that the paper should be square when you start. You can always cut a rectangle piece into a square, but many specialty craft or paper stores will sell square paper for origami. This paper will be the right weight for making the folds, and have a nice finish for the product you are making. If you are making squares for something like a christmas tree, why not just try lots of sizes of paper and see what works best!