Arduino and sound capture are not a good choice. The throughput of audio is way too high to work well on an Arduino. It *can* be made to do telephone-level quality, but it's the wrong tool for the job IMO.
You can just use your regular computer microphone to record sound. You can use one of a zillion libraries (PortAudio, for example) or go directly to the platform API (depending on your platform -- Windows, Linux, MacOS X?) You could also use a USB microphone. If the computer needs to be small, look at a Raspberry Pi plus a USB microphone.
For wireless transmission, use WiFi. Transmit a UDP packet per buffer of audio you receive in the audio recording API.