I'll attempt to walk you through without screenshots.
Video
Open up MeGUI. It doesn't work on a straight input file, but rather on AviSynth scripts.
Tools > AVS Script Creator
Set Video Input to your raw "animation.avi" video. It will preview it for you to make sure it's reading it correctly. Go to the Edit tab and add "ConvertToYV12()" to a new line at the end of the script.
Save the script as "animation.avs".
Now that you're back to the main MeGUI window, set your Video file format to RAWAVC and choose an output file, something like "animation.264". In the encoder settings, choose the preset "x264 Unrestricted 2pass balanced", and then go into Config. Don't worry: you only need to bother with one setting---the bitrate. I used 2700 kbps. Higher bitrates offer better quality. Anything over 5000 kbps is excessive. If you have a target file size,
calculate the bitrate you need.
If you don't have this so-called "x264 Unrestricted 2pass balanced" preset, just use the default x264 settings with 2pass encoding turned on and the bitrate of your choice.
Hit that "Enqueue" button.
Audio
Audio is more straightforward. For Audio Input, choose your uncompressed "animation.wav" file. For the extension, choose "Raw-AAC". Choose an output file name like "animation.aac". For the encoder settings, choose FAAC and Config it with ABR and a bitrate of 128.
Hit that "Enqueue" button.
Encoding
Your jobs are now queued up to be processed. On MeGUI's "Queue" tab, look at the list. There should be three jobs: two video passes and the audio encoding. Run the jobs with the Start button at the bottom, and wait for them to run.