.avi is a container for a variety of codecs, the most popular being Divx and Xvid, which are varieties of the MPEG-4 codec.
MPEG-4 is a codec which also comes in many clothes, H264 for example, or the aforementioned Divx/Xvid.
Those MPEG-4 codecs are for content distribution, maximum visible image quality with a minimum of file size.
YouTube currently uses the MPEG-4 codec variant called H264, so you should be fine if you use that and use the proper settings (enough bit-rate and maybe even more than one pass of encoding).
For your information, FCE can use many export settings, many of them will result in very big files (1GB/min).
If you finally get FCE you can try two ways of exporting.
1. FCE with settings to export to a H264 encoded video file
or
2. FCE to export with settings to export to a big a not MPEG-4 compressed file, and then use MPEG Streamclip (or some other software) to convert that big file to a smaller H264 encoded video.