FerFal -- first, thanks for your writeup on the situation in Argentina from a couple years ago (seen on other forums). It's insightful and I got a lot out of it.
Here's the situation regarding aliens and firearms. Non-resident aliens (i.e. those without a green card) are prohibited persons, unless they fall within a few excepted categories... one of which being if they possess a valid state hunting license. So, as a non-resident alien you're okay with the feds if you get a cheap small game hunting license, and make sure to renew it every year before it expires.
Resident aliens (green card holders) have the same 2nd amendment rights as anyone else.
The law is a bit more subtle than this, as non-resident aliens are properly classified by their immigration or visa category rather than merely the possession of a green card; but I think my overview is largely correct.
Avoid Washington state, which requires aliens to have a special license that is no longer issued, and of course avoid the 6 "bad" states (California, Massachusetts, Illinois, New York, New Jersey, and Maryland IIRC).
New Mexico has good firearms laws, but does not allow non-citizens to obtain a CCW permit. Fortunately, aliens can obtain a Utah non-resident CCW permit, which is valid in many western states. California doesn't discriminate against aliens in state law, but carry of any sort is generally not permitted in CA at the moment. I don't have any state specifics aside from that.