You shouldn't really need any tools for your AR, if you're just gonna shoot it... if you're planning on minor gunsmithing, or just swapping out parts, the castle nut wrench, an armourers tool (for the barrel and muzzle break), and some roll pin punches would all be pretty useful... at least then you can perform some maintenance on it if required. Just a word of advice, don't buy the brass roll pin punches from princess auto, they're too soft and the tips start to warp after a while... all that stuff mentioned can be had from Brownells, also... since they're considered tools, they don't necessarily fall under the firearms parts category, so the 100$ restriction shouldn't apply.
Problem is, (and I'm not sure if it's entirely a problem yet) is that gunsmithing is somewhat addictive, well I found at least, once you start tinkering with your gun, then you just can't stop until it's that "perfect" dream gun you've always wanted...