You do not need Compressor for iPads or YouTube/Facebook/Vimeo. That is all built in to FCP X.
For DVDSP you have two options. Send it to Compressor to manually set the controls and encode your MPEG2 vidoe and AC3 audio files for DVDSP.
This page has an old 3-part tutorial walking you throught this whole process from legacy FCP, but applies the same to X. Look under the "FREE Legacy Tutorials" section.
Otherwise you can save out to ProRes 422 and let DVDSP encode the media itself. Yet for best quality, follow the instructions in the videos. Nothing wrong with either way.
People will tell you that encoding in Compressor will give the best quality, but that assumes you are using a suitable preset and for your length of video the ready made ones are unsuitable and will waste time as they are all 2-pass with variable bit rates (VBR).
For DVDs under 70 minutes long the best quality and fastest encoding times are achieved using a constant bit rate (CBR) of around 7.5mbps.
For your short DVDs you should achieve the highest quality and fastest processing by simply exporting the project from the timeline as it is, drop it into DVDSP and set DVDSP to encode and burn it at the specs I gave above.
Returning to my opening comment, you will frequently find that the theoretically best solution to a problem results in no discernible improvement but often entails a lot more work and time-expenditure.
P.S. You might get marginally better quality by raising the bit rate to 8mbps but you run a slight risk that some old or cheap players may not be able to keep up, resulting in dropped frames.
Message was edited by: Ian R. Brown