Ok, some good advice, and some very bad advice on here. Arrows have a spine rating, this is a measure of how stiff the arrows are. As suggested above, I also suggest starting with aluminum. They have very good tolerances, another feature of arrows that I'll talk about in a bit, quite durable, and cheap. Some carbon shafts, like the one I'm shooting now, are more durable than aluminums, but there are plenty of carbon shafts out there that are nowhere near as durable.
Another advantage with aluminum is that it's easier to work on, putting points or nocks on aluminum shaft is a lot hassle free than carbon. So if you later on decide to work on your arrows yourself, it's something to consider.
Now, spine. With aluminums for every given draw weight and draw length combination, you have 2 or 3 spine sizes that will match you. Usually one is light weight and the other one heavy weight. Aluminum shaft sizes come in a 4 digit number, for instance 1716, 1714, 2014, 2012, and so on. The first two digits tell you the diameter of the shaft, the last two digits is the thickness of the wall. So a 1716 shaft has 17/64" outer diameter and a 16/1000" wall thickness. The thicker the wall the heavier the arrow, but also the more durable it is. Sometimes for a given draw weight and draw length you can get a choice, say a 1712 or a 1614. They're both the same spine, the 1712 is lighter but less durable than the 1614. Go here, this is the Easton archery website
http://www.eastonarchery.com/products/selection-target
Put in your bow weight and draw length, it'll tell you what size shaft to get. Stick with the Easton Platinum Plus for starter, about $50 for 12 arrows already made. The Platinum Plus might be cheap, but until very recently it holds the world indoor record at 25m.
Now tolerances. Arrows have different tolerances, straightness, weight, and spine. Out of the three you'll see straightness and weight tolerance usually mentioned by manufacturer. These two are somewhat good indicators of how good arrows are. Aluminum shafts from easton usually have a straightness tolerance of about 0.001" and weight tolerance of around .75%. Carbons on the other hand, if you buy a set that cost $100, you get straightness tolerance of 0.003". The biggest impact to your shooting however is the spine tolerance, and it's the one that manufacturers don't talk about. If you're shooting compound, the spine tolerance is not much of a problem, but it is a big deal with recurves. Aluminums also shine here, until you get to the high end carbons where a set cost you $180 up to $350 just for the shaft.