It depends.
Dad is left eye dominant and right handed and shoots everything as a righty except for bench shooting a rifle. Shoots really well. Learned to do it right handed because folks handed him right-handed equipment. Never switched over because he sees fine out of his non-dominant eye, can buy right handed gear easier than left, and since he's right handed stuff like controls on a weapon or quick, offhand shots are easier that way.
His boss is the opposite. Lefty who is right eye dominant and has shot right handed weapons his whole life. He also shoots right handed. He has much better vision in his right eye, and also learned to shoot that way because growing up he got handed right handed weapons. His wife bought him a really nice left-handed Browning rifle after their business took off and he took it hunting for one season and then sold it for a right handed model.
Different people are different degrees of eye/hand dominant. I don't think you'll know for sure what you like until you try it for a bit. Generally, when I worked in a shop I'd advise going right-handed if at all possible just because of bow and accessory availability. Also, if you rely on somebody else to tune your bow, good luck finding a left handed bow tech.
