Your first instructor rating will be your "initial instructor ride", your FSDO may require or prefer that you take this ride with a fed rather than a DPE, you will cover the FOI theory on this ride, and you you might be held to a higher standard since this checkride elevates you to the instructor ranks.
You can do any rating you want first. Folks usually do the CFI, but some schools actually steer their students towards the CFII, for the reasons mentioned above.
I trained one guy who only wanted a CFII, and never bothered with other ratings.