Not much I can say from my own experience but I have had friends who have gone a similar route. I don't know all the details but this should be able to get you started. Firstly I would like to mention that while mechanics here don't really get paid all that much, at least here in California they don't. With the sky high rent and whatnot. I currently make $25 an hour and the average is around $20 unless you go work for a dealership. Then I believe it is up to $40 per hour. (For a starting mechanic with some training) Barely enough to offset rent in cali.

Just a word of warning as it was my dream job and still is, but if you are talking financials you gotta be able to offset the cost. Starting mechanics on average get minimum wage with no training or experience, so it's good you decided to go to school first. I would also recommend that if you plan to go this route to find something to specialize in. And then work through other things later. For example it is very easy to get a smog license. 3 months time and one test and you are certified. any other courses like basic engines, suspension, transmission, fuel are going to be a little bit longer on time if you are going to be in a trade school or community collage. I would personally recommend community collage over trade school as both are about the same cost, but trade school can't always guarantee you a job. I was right out of my community collage though and still get emails to this day for places that are  hiring mechanics.

That put of the way, I would research looking into a student visa. As I hear it is the easiest way of getting into the US and you can extend your residency pretty much as long as you are in school. In terms of jobs, around colleges is probably where you would want to be around to start, and around campus was always busy and had a steady need for people, that way your job could legitimately be next to or in school. If you want money fast, a burger joint like in&out here in California would get you cash pretty quickly and it is very easy to get promoted. 

Anyways. People like to see talent so after you find out what your specialize in, and finish that, moving on to the next thing, then that's when you can start looking into being a real mechanic. I got really lucky or unlucky? Haha I started fresh out the door as a benz and bmw tech but my major was in suspension work. Ehhh whoops lol. I got greatly intrigued by computer technology while learning how to use the STAR system and whatnot, and then went back to school to learn about hybrid systems and EV's. On the job, I learned the basics of engine and trans, since I didn't know, I was a suspension tech after all. But eventually got my AA in engine basics as well. That being said, if you got the cash for it saved up, permanent residents isn't that hard just tedious as hell. Just a lot of government paperwork and fees, and you probably going to be renting until it all comes through, or marry into a family haha.

The job for me personally is a job but I am always looking forward to see what's gonna happen that day. Be it just oil changes or engine overhaul. Sometimes something really frustrating like a Benz sprinter turbo. By the book be hella bs when it comes to rust and frozen parts that shatter to pieces haha. Sometimes funny things too. It's a great work environment for me personally as I tend to raise my voice as I talk being southern Chinese and all and no one bats an eye. Attitude is everything from what I understand this far. And also don't feel pressured to know everything. Even on this form people got their own specific ways and specialties. That said again, I wish you the best of luck!