I think I can help you out on this subject. I'm Portuguese and just arrived in March from the States where I spent 2 years studying and working as a CFI. I went on a J1 visa that no longer exists, but at the time was the only visa that allowed you to work. Now the F1 has replaced it. The main points about the F1 are that you have up to 5 years to finish the course (i think), a really long time, and then one whole year to work as a CFI. You won't get a F1 visa if you have flight experience over a PPL. I've seen European students being rejected because they had an ATPL theory with 250hrs, but other being accepted with 50. The M1 visa is another type that doesn't allow you to work, just study. There are very few schools that are allowed to issue F1 visas and they only do so on the basis that you will complete the whole course which could be around 40,000$. I've heard of some smaller schools that can issue M1 that do so to Europeans and then hire them illegally as CFIs. If you get caught you're screwed.
I was working in Oregon where the weather isn't great but the school was big so I was able to get a lot of hours considering I only worked for 13 months. The school where I was working normally employs students to work as CFI, they have a lot of students and are constantly hiring! If you already have an ATPL then you're only option in the States is either to go with a Green Card or just for time building.