In my experience the best way to get a round pie is to start out with a dough ball that is round. That is, don't store the dough in a square or rectangular container and don't cut it out of a larger piece of dough such that you end up with an oddball shaped piece of dough. Once you get the dough ball on the bench and start to work with it to form a pizza round, gently flatten the dough into a disk shape and press the dough outwardly from the center, using your fingers. When you have opened up the dough sufficiently using your fingers, say, to 10" for a 12" pizza, you can then lift the dough and stretch it out to the final desired diameter, draping the dough over closed fists and rotating the dough while you stretch it using your fists. You have to do this in a symmetrical, rhythmic manner so that the dough round doesn't become lopsided and assume a shape other than a round one. To do this successfully requires practice, practice and, finally, practice.
I don't know what you mean exactly by a "floury taste" but if you are referring to a raw flour taste, the best way to avoid that is to use minimal flour when you are shaping the dough. It is OK to drop your dough ball into flour to overcome any surface moisture, but you should then shake off any excess and not go overboard with flour on your work surface. Otherwise you can end up with a bitter taste in the crust because of the way that raw flour bakes up in the oven. You might also end up with a floury taste if the crust isn't baked enough, if that is what you have in mind.
As for the best cheese, that is strictly a matter of personal preference although a whole-milk mozzarella cheese will usually bake up better in the oven and usually won't develop a brown crusty top as you might get with the low-fat version, or as quickly. Whole-milk mozzarella cheese has more fat, so if you are concerned about that you can always use the low-fat version. The whole-milk mozzarella tends to have a more buttery and rich taste, mainly because of the higher fat content. The best way to answer your own question is to try both and see which you prefer. Some people compromise by using a blend of both the whole-milk and low-fat cheeses.