I think using the Wi-Fi would complicate things for a task as simple as this, as as rolling your own Wi-Fi stuff is not so easy, so unless you are set on that route I would consider other easier options first. However here is a page with some Microchip Wi-Fi solutions (check the dev boards out at the bottom, you could maybe get the PICdem board and the Wi-Fi plugin)
Probably pretty involved if you have no prior experience with uCs, I haven't used their Wi-Fi stack but I have used e.g. their USB/Graphics stack, and they take quite a bit of getting up to speed with.
FWIW, a one way intercom could be made with a few transistors, passive components, 9V batteries and a small mic/speaker. Google for things like "FM bug circuit" (example here) or "Walkie talkie circuit" and you will get hundreds of examples that you could adapt to your liking. You could also use the circuit with a uC in place of the modules suggested below.
It could also be made with a couple of RF modules and microcontrollers. I would recommend something like a PIC16F or 18F, and something like one of the options on this page. I would go for something simple like this one rather than e.g. xBee as no messing about learning a new protocol, rather you can come up with your own simple one and drive from UART or SPI. You could probably even forget the uC on the other end and just PWM the audio through, and have a filter, opamp and a speaker at the other end (here is an example of PWM/filter/speaker, you would just have to add the RF modules and opamp)
For the microphone, it would connect to an opamp, then to the PICs ADC to transmit the data (either PCM then PIC+DAC at other side, or PWM direct)