What are some really good cameras for videos AND pictures?

I'm looking to start a career online and I need a really, really good video camera that takes amazing-quality videos and crisp, clear pictures. I know certain makes come with remotes that you can control the zoom, play, and stop features from and one of those would be awesome but it's not really a necessity. See the following videos for a quality reference:

I want something with really good audio quality as well. I'm willing to pay up to about $600, but seeing as I have a lot of particular requests as to what I need, I will pay more for a camera with all the fabulous qualities I'm looking for. Preferably Canon or Nikon, but it's not a definite necessity.

Please help, anyone who knows of a really good brand and make. I'm desperately looking for the perfect camera to start my blog and youtube channel and I want all of my photos and videos to have beautiful, professional quality.

(One more request--make sure it's not too big for me to take it in public! I'll be traveling with it a lot once I get more money.)

Nikon D3100 or D5000. Nikons are basically the best so even if you don't want these you should definitely get a nikon. They have great sound quality and HD video quality and take very clear HQ pics.

I'm a videographer. I suggest you have two choice can fit your budget and get the result like her video.
(1) a really good second hand HDV camera (very likely on tape), you connect directly to your computer and operate from there. You can record it without any tape, so here you save time and money.
(3) a DSLR that shoots video. You need at least 3 months of learning online until you can fully master it. It does not come easy - I had to take 6 months to really fully understand how my camera reacts.
p.s the video you showed is not great quality. She could use a HD webcam to achieve this.