You are starting on a slippery slope...you have been warned
Rod size - depends on your average fish. If you are going up against 5lb fish with the occasional 10lb'er....a 6wt. 10lb average with the occasional upper teen fish...a 7 would work. Anything above that an 8 is the way to go. The biggest reason for the heavier rod is so you have enough backbone to turn that fish around - if you don't, he will just keep going...and going...and going
Leader/tippet - I typically go with 6 to 7 feet of level leader (6 to 12lb test)
Must have flies - backstabber, carp carrot (soft hackle), egg pattern, a few natural nymphs, and some top water stuff for the occasional opportunity when they are surface feeding (caddis, mayfly, stimmies, etc...)
Extra gear - a net is handy as is a scale. Dont forget sun protection. The best carp fishing is during the brightest and hottest weather.
Strategies for hooking up - it takes practice but 99% of my carp fishing is all visual. The more you do it, the more you will recognize a take.
Once your hooked - just hang on. For the most part, the fish is in control or your leader (or rod) will be snapping. Put enough pressure to slow them down and they will usually cooperate. After the first run, they are typically a bulldogish fight with a lot of give and take.