As mentioned, the SDK is free, but to sell/give away apps, or to install on hardware, you need to register and pay the $99/year.
Other than that, you'll need an iPhone or, at least, an iPod Touch. The simulator (available with the free registration) works pretty well, but if you're serious about development, you want actual hardware to install it on.
So, at a minimum, if you truly want to develop, I'd say the $99 developer registration, a sub-$200 refurb/used Touch, and a couple of Objective-C and/or iPhone development books. The books you can do without, but I think they're worth the money. So, say, $200-$400 required.