iPhone app to support my study

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Hello people, Here is the situation: I'm a student Informatica in my first year. Now I had the idea to make a new iPhone application that isn't out there. But there's a few points I'm not really sure about, so I though why not ask all of you what you think about this. First off, if I even want to start creating the application I need to have a Mac OS X running on my computer. I'm running windows right now so I'd either have to dual-boot Mac or buy a whole new computer (which is really expensive and I'm just a poor student!) Second, say I do get a Mac and am actually able to program on it, I need an idea. Badly. I'm seriously doubting about making this application a game or not. What do you guys think? A nice puzzle game? Or some educational might-come-in-handy app? Then thirdly, there's the app store. From what I've heard you need to pay a one time fee to be able to upload your apps to the app store. Completely understandable, but I believe it is quite a big amount of money (for a solo noob programmer anyway), so do you think I should still do it? Wait untill I have a great idea worked out perhaps? On the other hand I really think that programming an application for the iPhone would really support me in my study, so that really is a plus to me, but is it good enough compared to the other doubts I have..? I need you wisdom, enlighten me! Thank you in advance!