The Xbox 360 is possibly one of the most well-known systems, partly because of killer games, including Halo 3 and Halo: Reach, Fable II, Fable III, and others, and partly because of the famous Red Ring of Death (RRoD for short). This system has received mixed reviews, some praising it for it's graphics (which are killer, by the way), some saying it's as good as garbage with the whole RRoD thing. In my opinion, if your smart with it, or buy the newer version which doesn't get RRoD, then you should be fine and have an awesome system that you can be proud to spend $300.00 to $500.00 on. As far as game goes, it's like it's older brother: Mainly for older gamers. Not exactly a "child friendly" system.
As far as the Red Ring of Death, here's what happens: The internal fan is (well, was) improperly placed, so the motherboard and circuitry got hot, warped, and bang! Puddle of plastic and circuits! Ok, well, maybe not THAT drastic, but still, it could get hot, so don't touch! For avoidence, well... There's really no way to avoid it. Try putting it in a nice and ventalated area, then you could get somewhere. Otherwise, just sit tight, cross your fingers, and hope for the best.
The price ranges from $300.00 to $500.00 at GameStop for these puppies.