Getting 300MB of video down under 10MB is going to be really difficult to do without dramatically affecting quality. My advice would be to first edit down your demo reel to just the most representative sections of your work. If you're looking for work in character animation, those companies aren't going to care about seeing flying logos, text dancing around, that sort of thing. They want to see natural character movement like a really good walk cycle. Remove all extraneous material from your demo reel so it's short, snappy and with no "fat". There are some good tips about creating a demo reel on these sites (some are a bit old but the advice is still good):
http://www.cgauiwtalk.com/showthread.php?t=5334
http://www.edharriss.com/getajob/all_pages.htm
http://www.kenstone.net/fcphomepage/demoreel.html
http://animation.about.com/od/educationresources/a/animdemreel.htm
Once you get the reel down to it's essentials, then you can see what you can do about compression. I'd suggest starting by using the h.264 codec. It's going to have a good balance of compression size versus quality. Then look at frame size; when demoing animation I'd prefer to reduce frame size rather than dropping the frame rate too much. Then if you have an audio track, use a low bit rate on it; 128 kbps maximum should be sufficient and 64 kbps might be good enough. A company hiring an animator isn't going to care about your audio track's quality, and might not even want to hear one so you might consider removing it altogether.
Someone else here might have some additional tips, but I hope this helps.