I would advise consulting with an experienced immigration attorney about the best immigration options for your fiancee. If you file an I-130 Petition on behalf of your fiancee, and she seeks to consular process her visa, she may have issues with her travels as a visitor to the United States. U.S. Customs and Border Protection (CBP) may claim your fiancee has immigrant (permanent) intent to remain in the United States because she has an I-130 Petition filed on her behalf. She can present proof of her home country ties to the UK, and explain that her current visit is for temporary purposes. Of course, the decision to allow your fiancee to enter as a visitor (with an I-130 Petition pending) is with U.S. CBP.
She probably will not be able to travel well her application is processing. I would highly recommend you hire an immigration attorney to file this for you. They can't speed up the application per se but having it properly filed will ensure there are no delays, which are likely if you try to do it yourself. My firm handles such cases.
Law Offices of Nicklaus Misiti
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Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.
Consult with an immigration attorney to ensure that your application is properly filled. If you are going to get married next month, and then enter the US in January, you may think about getting the K-3 visa and filing the paperwork in the US. However, the US embassy may say that since you are married, you should file for permanent residency for your fiance/wife as opposed to getting a visa. Once you enter the US, I would advise that you finish all the necessary applications before travelling back and forth, unless there is a medical emergency.
The process involved with sponsoring your future spouse for permanent residency depends on where you currently reside. I would suggest you contact an immigration lawyer for specific advice. I am based in London, UK and would be happy to assist you and your fiance.
Please note that by answering this question an attorney client relationship is not created. My answer is general information based on the facts provided in the question. Detailed and accurate advice may only be given once a lawyer is able to meet with a person to assess the totality of a person's circumstances.