The simplest way to record a live stream is to set the StreamType to "live-record" in your Application.xml file.
This gives you very little control over the recording process.
By default the recorded files will be .flv. To record to mp4, you add "mp4:" prefix to stream name in the encoder (or StreamManager in the case of MediaCaster streams), then Wowza records to mp4 container.
Stream name "mp4:myStream" will record to myStream.mp4
You can publish a stream from a Flash based application and play it back in a Flash based client with out using the Wowza Transcoder.
The default video is Sorenson Spark and NellyMoser audio which are not supported in non-Flash clients.
To make the video quality better you can follow this guide to set the video to H.264.
And if you want to play back the stream in non-Flash based clients you will need to change the audio from Nellymoser to Speex in your Flash application, and use the Wowza Transcoder to transcode the audio from Speex to AAC audio. again, this article explains these steps: