the fiancé visa application was really thorough as you would expect. But it will be no different than a marriage visa application. Lots of questions about her family, when did you meet, how, where, etc etc. You have to show photos of you together. Call logs, chat logs. Basically you are proving you truly know each other. I showed multiple itineraries from trips to Thailand.
Once approved we went to Hawaii where I was living and got married literally the next day. Then we could apply for her green card. That also only took 4 months.
According to the lawyer I used it was considerably easier to do it as a fiancé than if we got married in Thailand and applied that way. So I would recommend a fiancé visa based on that.
As far as her traveling with you it certainly makes it easier for her to obtain visas as the souse of an American than as a single Thai lady. But she’ll still fall under the rules of a Thai until she gets that blue passport.
One good thing is when entering the states from abroad they don’t separate you. They literally said “we don’t separate families. So even if your wife is not a citizen you go to the American citizens line.”
For reference: When my wife did her interview for her fiancé visa she was pretty far down the line. She guessed 20 ladies went in before her. Most were for tourist visa 1-2 for fiancé. If I remember correctly all but one were denied.
Next to impossible if she doesn’t have all that Garrett outlined already.