You need a floating fly line, ideally a Weight Forward line, or failing that a Double Taper line. The line size (weight) should be AFTM 7 or 8. As for the fly rod, one about 9ft long will be suitable, rated at AFTM 7 or 8. You could manage with an AFTM 6 rod at a pinch.
Buy a tapered leader with a minimum breaking strain of about 8 to 10 lbs. For the tippet - the final section of line, about 3ft, to which you tie the fly - use 8 or 10 bs nylon. Drennan nylon is good. I've tried fluorocarbon line as a tippet, it's expensive and didn't increase the number of takes I got.
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You could buy a more expensive fly line, although I don't think it's necessary for carp fishing. I've got a Rio Grand floating WF7 line, now renamed Grand Premier. It's got a slick surface, and a special taper at the front end which gives extra weight and makes it easier to cast into the wind. But it costs £90.
I've tried using deer hair flies cast with a carp controller on a carp rod, without any success. I find it's better to use a large edible floater with a conventional carp rod. I can cast it about 10 yds, if I need any more distance I add a carp controller. I've seen carp ignore floaters on a hook cast to the middle of the lake, but will readily take free offerings. They can tell the difference.
I catch more carp by using floaters cast towards reed fringed banks, or small islands. The nearer the floater is to the reeds, you're more likely to get a take.