I don't know your market so if you feel the MEI is going to net you more cash after you get it then go for that first. Clearly money is an issue for you. Personally, I don't know of anyone who started flight training in a multi-engine. Frankly, I don't think any flight school offers this as the recommended starting point. Thus, getting that MEI, while at fuel cost, may be useless. What this means is that you'll spend more money to add the single-engine, before you even make a dime.

If I were you, I'd get my CFI, CFII, then MEI. Fast money is at the CFI level. If you are smart about this, you'll heed the advice of doing your ground work first before you even engage an instructor for the flight portion. CFI is about teaching. If you can't explain and transfer knowledge, I don't care if you're Chuck Yaeger, you are going to fail as a flight instructor. This means you have a LOT of ground work to do, which can be done at a bare minimum of cost to you.

And I would take the check ride at the FSDO. If you're prepared and ready, you're not going to get the pink slip. I walked into the FSDO knowing that CFI certificate was mine and all the time spent with the inspector was a formality because I studied hard and meticulously prepared. 4 hours later it was a done deal. I'd like to say that the CFI I used for ground preparation helped but that would be a lie. His biggest contribution was signing the endorsement in my logbook. The rest I figured out all by myself and am considered one of the better instructors at the flight school I operate out of. I'm not saying this to toot my own horn. I'm just demonstrating that you can do about 90% of the CFI all by yourself. If you have any questions, feel free to PM me.