He is new to AR 15s...so can you give a little more info rather than rephrase his question.DO you stock 5.56? If not what calibers do you have that you can get a AR in?
Mac--- AR 15 comes in many different calibers. However, you asked for one that is cheap to shoot and accurate to 200 yards.
5.56/.223 meets the criteria the cheapest. Get a Wylde spec chamber and you can use either 5.56 Nato or .223 ammo in it. Ammo can be found nearly everywhere. Magazines are cheap.
7.62x39 runs neck and neck in price as 5.56/.223 and should be ok at 200 yards, although some cheaper ammo may not be as accurate as you want. 7.62x39 AR 15 can be frustrating as I hear about a higher percentage of issues in cycling in this chambering.
The 9mm AR 15 won't be accurate at 200 yards, and energy levels will be anemic at that distance.