When you started the discussion I was under the impression that you go to a Yeshiva that is more Yeshivish than your upbringing. In that case, there is no greater point to bring up other than that you want to fit in with your crowd. If that is not the case, and you just like the idea of a hat, perhaps you should try to understand what your father is trying to convey to you. It really is silly to just put on a hat because of what you like about it, when it will make you stand out.
You mention the idea of the mindset it will give you by Davening, and the seriousness it impresses upon you. Don’t think you won’t get used to it. After a while it becomes like any other clothing, unless you reserve it for the occasion. Remember, when in Rome you do as the Romans do.