It is visa fraud to enter the U.S. on a tourist visa with the intention of adjusting status in the U.S.
If you want her to be together with you the quickest, you should not get married yet, apply for a fiance visa, and then get married here, and then apply to adjust status.
The other option is to get married (anywhere), and then you file I-130 petition, and she goes through consular processing. The whole process takes a year