Private, Instrument, Commercial, ME, CFI, CFII, MEI.
There are variations to that route depending on ones perceived benefits to doing so but that is a traditional route.
That is the traditional route - doesn't mean it's always the best. Someone mentioned possible benefits throwing commercial sea plane in there to meet complex requirements.
I personally did it MEI -> CFI -> CFII. I had planned to do the II second and CFI third, but there were scheduling conflicts that screwed that up.
One advantage of MEI first is that you can take the other CFI rides in in a non-complex plane which should save a bunch of money. Not being limited to complex planes means you'll have more plane and instructor options open to you. That was a huge plus for me since I wanted to pick the best instructor I could find rather than being force to pick from the few who had access to complex planes. There happens to be a complex single at the local airport, but their instructor at the time was horrible and they wouldn't let me bring in my own instructor.
Another advantage of MEI first comes from the fact that you're required to have 15 hours multi-PIC to take the exam. Odds are no one's gonna let you rent a twin solo with the 8 or so hours of multi time it took to get you commercial, so you're spending that 15 hours with an instructor anyway. If you go CFI-single first, you're spending a bunch of money learning to teach in a single and then you still have to spend 15 hours in the twin with an instructor before you can take the MEI exam. Instead, spend that 15 hours in the twin learning to teach in the plane and save all the money you would have spent learning to teach in the single.
If you're good, you can check off some or all of the CFII training during the 15 hours of multi-PIC you're doing anyway.
There are some downsides to doing the MEI first:
* It's more money upfront (but less in total).
* Some people get a CFI job and their company pays for their MEI or they find ways to grab free multi-PIC hours to count towards the 15. If you do your MEI first, that's not really an option.
* It may be (much) harder to schedule the checkrides.
In my case, the FSDO here farms out initial instructor rides to DPEs, but they made me take the MEI ride with them since it was an unusual case. Took 2 months to schedule. Up side was exam was free!
Then there was no one in the state qualified to do a single engine CFI
add-on exam, so I had to do that with the FAA observing while the DPE got qualified to do single add-on rides. Took 6 weeks to find a time that worked for me, the DPE, the FAA, and the weather. The DPE agreed to a reduced rate given the circumstances, so I came out ahead there too.
Despite the hassles, I would do it this way again and not just for the cost savings. I feel I got better training and I think I earned a lot of respect from the FSDO and examiners in the area for pulling this off.
EDIT: looks like I covered some items the OP said to disregard... oops. For the issues he did care about, I saved the cost of about 1.5 checkrides this way, but that might not be typical. I also avoided virtually all dual for the CFI ride in a single engine plane. That probably is typical.
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