Yes, he entered on a tourist visa, and after a couple of weeks we went forward and applied for his green card. We did not get married in the US and the US recongnizes the validity of our marriage in Argentina.
There are two things you can apply for in conjunction, one is to work (which really only came through about 10 days before the green card), and another to travel, so that if he had to leave the country he would have no problems returning to the US since he was sort of in limbo status between tourist and permanent resident.
We moved with our son (almost 4, born in Argentina but with US citizenship) and a dog.
That is correct that my husband couldn't work until the green card/employment permission came through, though we were aware of this and it wasn't a problem at all.
I considered using a lawyer, but honestly if you read everything carefully I don't think it's necessary. Visa journey was helpful (though I definitely didn't read everything as it can become a bit scary), as was the USCIS website.