I am relatively new to fly fishing and haven't fished for carp, myself. But here are some thoughts. I would imagine you would need a pretty sturdy set-up for carp---something like a 6 wt rod. You can get some decent setups from Cabelas, Bass Pro or Dick's Sporting Goods for like $50-$60. They come all set (rod, reel, prespooled with backing and fly line). You might have to buy some tapered leaders, though. My first one was a 5-6wt 8ft rod, Cortland brand. I like it a lot. Good thing about these sizes are that they are pretty versatile---You can go for lots of species of fish with them. I go for panfish, trout, and bass. The length of the rod is something to think about IMO...if there is a lot of cover where you are fishing, a shorter length may be better. I am sure there are others that could give you some feedback on that.
I am interested in hearing about how you do. I have seen a lot of carp in the stream where i fish, but do not know what flies they like to eat.
Anyway---hope this helps and good luck!!