Would someone point me to the direction on how to render a video (.mov) extension (mp4) and be able to maintain max quality? On top of that, I was trying to smooth out a motion using http://www.videocopilot.net/tutorials/stabilize_shaky_footage. I tested both outputs with or without the motion stabilization method here, the quality degradation is unacceptable.
Don't use AE to make your MP4 Render lossless and then compress in another program. See Dave's answer below for more on that-
Dave's Stock Answer #3:
Don't use AE to compress files for final delivery. The various compressors are there only to make quick 'n dirty files showing a project's progress to producers, clients, the kids, etc. AE is incapable of doing multipass encoding, a crucial feature that greatly improves the image quality of H.264 and MPEG-type files in particular.
Render a high-quality file from AE, and use a different application to do the compression. Popular ones are Adobe Media Encoder, Sorenson Squeeze and Apple's Compressor, which comes bundled with Final Cut Suite. Even compressing in Quicktime Pro is better than compressing in AE.
Making good-looking compressed files is almost as much an art as it is a science. It is NOT straightforward at all. I recommend asking a few questions at the COW's Compression Techniques forum.