There is no fast way to immigrate; only faster ways. There is a possible undiscussed third option. I recommend that you both meet with an experienced immigration and visa attorney before you do anything. Otherwise, you may complicate matters.
A lawful permanent resident (green card holder) cannot petition a foreign spouse for what is called an immediate visa. Such first preference I-130 'petitions and visas' currently take over six years to process in Consulates. This is based upon visa quotas established in 1990. However, a U.S. Citizen can petition a foreign spouse for an immediate visa in the U.S. The application process is complicated.
There is some uncertainty with processing time for naturalization/citizenship applications at the Chicago District Office. Some naturalization applicants don't realize that they don't qualify. Mistakes can lead to delays, the loss of filing fees, and other challenges including deportation for a few.
A 'name check' delay can slow down your naturalization/citizenship application processing, even if other cases are moving quite efficiently. If a foreigner is lawfully present, then they may eventually overstay their I-94 entry card expiration and become unlawfully present. This 'may' cause serious problems particularly if they leave the U.S. at the wrong time.
The above is general information not meant to be legal advice. This reply does not create an attorney-client relationship.
