Agree. Do as much of the work as you can while working on your Commercial. It will prepare you very well for the Commercial SE and ME checkrides. You can get any of the flight instructor certificates first - MEI, CFII, or CFI. While it's most common to do the CFI work first, some schools will have you start with the CFII because there are less tasks to accomplish initially. They will then have you add on the CFI. The FAA (at least in FSDO-15, Orlando) takes a dim view to doing the MEI first because of lack of teaching experience (read: if you do the MEI first you WILL do it with a FAA Inspector and it will be a doosie).
However it will generally take at least 10 to 15 hours of dual and a large number of hours (40ish or more) of ground to complete the lesson plans and review them with an instructor.
The CFII usually can be done in about 10 hours of dual and 20 hours of ground and the MEI in about 5 hours of dual and 10 hours or so of ground. At least that's what I found worked when I taught it.