When should I use the Common Application? Should I apply online?

If a school is one of the 463 members of the Common Application, you are encouraged to use it. In addition to the obvious "green" advantage of saving paper, colleges prefer getting the materials online rather than opening and sorting thousands of envelopes.  It makes the process much less stressful for everyone because of the uniformity of the application form and because it takes less time to fill out one form for a large number of colleges, all of which pay a fee for the privilege of being member schools on the Common Application list and which pledge to treat both the Common Application and their own forms equally.

If it is at all possible, you should definitely apply online.  Some colleges have offered to waive or reduce the application fee for those who apply online, which could be a significant savings if you apply to a large number of schools.  And many schools will not accept paper applications anymore. See https://www.commonapp.org/CommonApp/FAQ.aspx for tips on applying online.  Be aware that it is not advisable to "mix and match" different formats in the application process.