Hallvard. It's not a bad idea at all. A Green Card and a Permanent Residency Card are the same thing. You get a Green Card (for a fee) when you become a permanent resident. A lot of jobs would be closed to you but by the time your contract is complete, you would be a US citizen, unless you deliberately choose not to.
From there you could attend university and go through NROTC. You would have quite a bit of financial assistance when you do choose to go to university and when you contract with NROTC you should not have much problems paying for your tuition either.
And from there if you commission as an officer, you would be getting paid more than your classmates who never served in the military since you would have 4 years Time in Service.
This is assuming of course, that NROTC goes well for you. And assuming that you want to stay in the military after 4 years of it. lol.
Just to clarify, when you enlist into the Army, odds are you will keep your job until your contract is over (which is in 4 years). 11B (infantry) is open to permanent residents so that is something you could look into if being a truck driver is not your thing. However, non-combat jobs are not a bad idea if you actually want to start taking college courses while you're in the Army to prepare yourself for university afterwards. ROTC and NROTC takes a lot of your time. So if you get many of the General Credit Requirement courses out of the way, you can just go ahead and take 12 college credits per semester instead of 16 or 18 etc.
Anyways, best of luck to you kardeshim.