"Marty Ross" wrote
Though my current budget doesn't really have room for it, I like
(2) best. I asked my instructor about this, and he thinks I
should do it. What he recommended that surprised me, however,
was to do the instrument-instructor first, since he says it's
easier than getting the CFI. What's up with that??

Again, improper use of terminology rears its ugly head.
First...no such thing as a CFI, we're just Flight Instructors
now.

Second...."airplane-single engine" and "instrument airplane"
are ratings on a Flight Instructor Certificate.

Third....He should have said.."Get your Flight Instructor
Certificate with an Instrument Airplane rating before you get
the Airplane Single-Engine rating.

Forth....Yes, you can be qualified to teach instrument flying
without being qualified to teach private or commercial students.

Bob Moore
Flight Instructor, ASE-IA