Multiple Country Visit

American man wants to take his Thai gf on a year long, multiple country vacation. They currently reside in Phuket. They want to visit the U.S., Canada, Mexico, South Africa, India, Egypt, Germany, and possibly other destinations. They will stay for a max of 60 days in each country (depending on visa rules) and are willing to alter their intinerary accordingly. He wants to know if it will be easier for her to travel as his gf (he would prefer not to get married for numerous reasons) or as his wife? What is the most practical way for them to go about obtaining the necessary visas for their trip? Thanks for the help...