Yes handholding a DSLR can indeed introduce shake but that's where a tripod comes in also I've seen some impressive
short clips accomplished without a tripod or other stabilizer just using a lens with built-in image stabilization or vibration control - not a solution for an interview, for that use a tripod.
My Canon T2i /550D allows me to view live video on the LCD at the back of the camera no problem. Can also, of course, play back previously recorded clips on the camera so I'm not sure what others told you.
Traditional videocameras do indeed have advantages over HD DSLR cameras and some filming situations are just not HD DSLR friendly. But overall, despite all the additional headaches, they are sooooooo worth it! :-) Budget wise you can't beat the price and the sensor size you'll get with a HD DSLR is HUGE compared to those found on a traditional videocamera. If you do decide on the HD DSLR route, I'd suggest buying either the T2i/550D, T3i or 7D
body onlyand then for the glass buying, ideally a 50mmm 1.4 lens from Canon or their cheaper 1.8 50mm if cost becomes an issue. There's so much other gear to buy but these bits will give you a sound, affordable foundation on which to build.
Steve Crow
Crow Digital Media
http://www.CrowDigitalMedia.com