Basically, I am wondering if I can just buy DFH and start recording, or if I need to buy EzDrummer then drumkit from hell.

So basically, is dfh an expansion pack for EzDrummer or no?
System req. from toontrack.com:

1 GB free hard disc space, DVD drive, A working EZdrummer® or Superior Drummer® 2.0 installation

So yes it's an expansion pack =)
Unless you can find a copy of the original DKFH sample set. It's a lot easier to use when you have EZ Drummer (or Superior Drummer) but the samples used in the expansion version are the same as were on the original sample set.
"If money is the root of all evil, I'd like to be a bad, bad man."

- Huey Lewis & the News
Just don't buy EZDrummer. It's vastly overrated. Get Steven Slate drums if you're going to buy anything. Sounds a ton better and will actually make you learn how to write drums.

Or just use some of the thousands and thousands of drums samples out there and learn how to sample.