You can either file for a fiance visa (which would allow your fiance to re-enter the US and marry you here), or you can wait until after you are married and file for a green card through consular process. The fact that your wife was formerly a student in the US should not be a problem, as it appears that she maintained legal status while she was here. Because the consular process is somewhat complicated and confusing, I recommend that you hire an experienced immigration attorney, to ensure that your case is prepared properly.
The location of the marriage ceremony does not affect the green card process. But you will have to be prepared with substantial documentation showing that yours is a bona fide relationship in the I-130 petition. Unfortunately, every marriage is flagged as suspicious, and it is up to you and your wife to prove that it is bona fide.