Lots of great information here.
Like Mark said, a cheap hand wrap reel will get you started. I've sure shot more than my share of carp with one. But if you'd like to "move up", so to speak, I highly suggest an AMS Retriever. I've been using the same one since around '91 or so and it's still going strong.
Definately get an AMS Safety Slide for your arrow though. Keep that line in front of the bow and you'll almost eliminate any chance of it becoming tangled in the bow string and flying back at you. Been there, done that.
You can get a strap-on mount for the retriever, or like CB suggested, some electrical tape works well too (I add a strip of rubber inner tube between the bow and reel though).