Yes, you need a Mac to build an app in Xcode (don't worry, there is lots of help for this on this forum).
Pretty much any Mac will work for you, as long as it is Intel based (I think).
I went for a Mac Mini (I had plenty of monitors, mice and keyboards to connect to it).
A Mac Mini is probably your least cost option, if you have the peripherals to connect to.
You will also need to sign up with Apple's iOS Developer program, $99/year.
EDIT: You will want enough memory to build, so the more the better. I don't think Apple makes a Mac device that doesn't have enough memory, disk, etc. to work with AppGameKit builds.
Cheers,
Ancient Lady