Looking to buy a HD Camcorder

I am planning to start a YouTube channel, and I already have most of the stuff, including editing PC and good audio recording equipment. The problem is I definitely need to get a decent camera. I did some testing with a cheap Sony CyberShot (Probably $80), and I want 1080p if possible, but the real issue is that the zoom on that camera sucks, and it is just not good for video. It also does not focus well with video, so I am looking to buy something in the $250 and under range that has decent video quality and zoom. Mic input is definitely a plus. I would like reasonably good battery life (1-2 hours is ideal). 1080p is important, but if it will cost a lot more then it is probably not necessary. 60fps is also important if it is not way more expensive. I looked at GoPros, but they don't have a zoom. What would be the best option in this price range. I know that I will probably have to make some compromises, and I will probably not get all that in a $250 camera. I am pretty inexperienced with camera stuff, so I was a bit unsure as far as what to buy.