In order to make "official" apps, that you can publish on the Apple app store and run on phones that have not been jailbroken, you'll need a Mac. Last I knew, you could download Apple's development kit for free, but in order to install apps on an actual iPhone or iPad (as opposed to on an emulator running on the Mac) or submit them to the app store, you'll need a developer subscription, which used to be around $100 a year and should still be in that general price range. The developer subscription also gives you access to extra information and tutorials.
No additional gadgets are needed, but you'll have to develop in Objective C using the Cocoa Touch SDK. I'm mostly a C++ and Java programmer, and found Objective C to be tedious and its syntax to be vaguely irritating, but that's just my opinion.