Which is faster and least expensive: getting married in another country or filling a fiance visa?

Significantly more information is needed in order to provide a legal analysis about processing times and costs. Beyond that, there are many details that are important to assessing pros and cons of immigration legal options. There really is no substitute for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.