The ongoing advice on this forum has been to export a Quicktime Movie (not quicktime conversion) using current settings. Make it self contained. You then have a movie file in the identical codec as the sequence and it happens quickly if all is rendered.
Take the movie file into Compressor and start with one of the presets that matches your requirements for a compressed file. If you have specific settings, Compressor lets you setup and save a custom setting so you can repeat the process in the future. By having the file out of FCP, you can go on with work and let Compressor render the file in the background. Compressor does a better job faster than letting FCP do a quicktime conversion, particularly if you enable best settings for resize scaling in the inspector under frame control tabs.
There have been lots of posts outlining the best way to setup Compressor for this task and opinions on the best codecs etc so a search of this forum should reveal a wealth of information and advice. It is a common question, particularly the workflow to make a DVD which is very similar so it has been included in the FAQ section (link at the top of the page below the handsome faces)