I like the h264 codec a lot. For videos on our team website, I've been exporting them as a Mpeg2 from premiere at the resolution that I want. I then run them through
HandBrake with a size entered (I use about 12-15mb for match videos. Longer Videos obviously need a larger size.). You can also just specify an average bit rate. Be sure it's doing 2 passes.
It doesn't get the integrated capture that you want, but it works pretty well. The key to getting high quality with h264 is having 2 pass encoding, I've found. The first pass analyzes the video so that the second pass can allocate the variable bit rate, giving a higher bit rate to the parts that need it while still keeping the specified average bit rate.