What kind of camera/camcorder is best for birth videography?

I'm already a photographer, but am considering getting into videography. I have a Nikon D90 that shoots video, but that's it since my d700 doesn't. Thinking about buying a HD camcorder or something of the sort. Any suggestions are appreciated!

Yeah

Look at the camcorders made by JVC, Panasonic, Sony and Canon.

Most of them shoot in Full HD, so finding an HD camcorder may be a challenge

From what I've read, going 4K would future proof your video capabilities. It could also be a source of repeat business. Most people have no way of viewing 4K video - yet. In the not so distant future, you could send out a promotion where people can re-order a copy of their videos in 4K.
Plus when editing you've got some cropping capabilities which allow you to do some creative editing techniques such as zooming in without loosing quality.

A entry level camcorder that can deliver quality HD video is the Canon Vixia HF R600. About $200. Will shoot both AVCHD for editing systems and MP4 for easy youtube upload. And has a microphone input, a nice bonus.

Why not start with your Nikon D90?

You have the good ones.