Need some info on filtering audio

Hello,
I am capturing a audio (baby's voice) with a mic. And I want to send it to micro-controller and then transmit it to a receiver wirelessly. So, I would like to know if I need to amplify the baby's voice and filter it in order to cancel out the background noise (it is a must to cancel out any background noise as much as possible).

If you amplify the signal you capture with the microphone, you'll amplify the background audio as well as the baby voice. Any noise generated by the following electronic circuitry would make a smaller contribution to the signal to noise ratio however.
I think what you want to do is some selective filtering with a bandpass, and maybe a notch filter (if there is significant background noise at in a small frequency range.
I'm not sure of the range of frequencies of your baby's voice, but I'd imagine you'll want 100Hz to maybe a few Khz maybe, or there about. A band-pass filter will suppress frequencies outside of your chosen range (baby's vocal range) improving the SNR.
It would be useful for you to record the background and look at an fft of the recording to see if there is significant noise at a single frequency, main hum, road noise etc., which a notch filter or two could take care of. These filters could be implemented in either the analogue or digital domains.