Flash 9r3 and above supports h264 and aac natively in an mp4 or f4v container. Any encoder that gives you that should work directly in flash.
If the video background is black, you will see black on the display whether through a browser or a video player. If you want it transparent, then you need to encode it with an alpha channel in vp6 in an FLV container put the flash swf into transparent mode in the web code. You can create the transparent FLV in either AE, or by encoding an avi with flash. This can be an ordeal the first time you do it. It's simpler to use a matching color.
Make the video/comp size the size specified by the web designer. 100-200px tall is fair for a logo.
Cory
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Corporate Video