A little background story first:

Here at home we recently have been getting nightly visits from an evil cat who belongs to a lady living across the road. The evil cat has been terrorizing both our two cats and the neighbor's one to a point that I already took my cats three times to the vet for shots due to open wounds caused by cat bites.

There is no other cat around, and the evil cat is so annoying that it will enter our house through the existing cat door and pick fights with our male cat right outside our bedroom door at 4AM. Not cool.

Because I lack the evil gene to simply douse the evil cat in gasoline and set fire to it, I have to go with the next best thing: a selective cat door. But upon research I've found no cat door cheaper than ~$300, which is mind-boggingly expensive, considering the cats also need to be tagged (~$100 each).

Being a true geek, what better pet project (get it? pet?) than to build my own fancy RFID-reading cat door?

So, how do I start? What should I read first and foremost? I've been reading a few projects on the web but each one uses different parts and I'm not sure what to make of them (probably because I'm after some specific).

What is the best range RFID reader for an Arduino-like board (and what board to get)?

Any input is appreciated!