This software has special requirements (for the video streaming and live interaction part, regular shared web hosting is not enough):   http://www.videowhisper.com/?p=Requirements ;
Options for the required rtmp hosting: http://www.videowhisper.com/?p=RTMP+Hosting ;
For affordable streaming bandwidth we recommend Red5 hosting: http://www.videowhisper.com/?p=Red5+Hosting Red5 plans are not recommended for archiving or recording.
On commercial production sites, achieve more complex functionality and performance with Wowza hosting:http://www.videowhisper.com/?p=Wowza+Media+Server+HostingAll Wowza plans are on faster 1000Mbs connected servers, more reliable, with extra features like optimized archiving, recording and rtmp stats.If you plan to use video stream recordings or archives we recommend using same physical server  both for web and rtmp so your web scripts can access the video files on rtmp server (for file management, ffmpeg conversion). 
You can use our rtmp hosting plans for everything (web+rtmp) or in combination with your other web hosting (install application on your site and configure it to use rtmp address from a plan you have with us). 
If you want to host yourself you'll need a VPS or Dedicated Server to install Red5. Our staff can provide Red5 installation: http://www.videowhisper.com/?p=Red5+Installation ;
If you have a big site or project, you'll probably need a managed dedicated red5/wowza server focused on bandwidth and connectivity:http://www.videowhisper.com/...Media+Server+Hosting;