As far as the selection of which handgun you wish to purchase, I can only assume that it's for defensive purposes. If that is the case, you really cannot go wrong with a Glock or a Springfield in any major caliber.
I personally am biased toward the .45 ACP cartridge and therefor suggest that everyone carry that round for self defense. I can only speak from experience, but Springfield XDs are excellent defensive combat handguns. They are well worth the money.
Now for your other question:
According to what I could find on this site, as long as you are an immigrant alien, you are okay under federal law. As far as obtaining a concealed weapons permit in New Mexico, it seems that the authorities will only issue you a license if you are a citizen of the United States.
The neat loophole around this would be that in New Mexico, there is no license required to carry a weapon openly (this is of course according to the map on this site). So it would seem that as long as you ahve immigrant alien status or have a green card, you are legal to possess a firearm in the US of A. In New Mexico, you are also allowed to carry it openly, however, you will not be allowed to conceal it until you have obtained American citizenship.
Hope this helps!!!
I am not a lawyer and am in no way responsible for any negative outcomes you may have from following this advice.