If you are taking your wife back to the United States and wish to get all the major paperwork out of the way then the CR1 visa or IR1 visa is the best way to go. They do cost a bit more and they take about 4 months longer however the amount of paperwork back in the US will be minimal. Most prefer to get the immigration out of their way as quickly as possible once and for all.
The CR1 Visa allows your Thai wife to enter the United States as a conditional permanent resident. This means that when she enters the US she already has her ‘Green Card’ and can work if she wants too. She is also allowed to remain indefinitely in the US. The conditional permanency holds for 2 years and she can apply to have this removed 90 days after the 2 years have expired.
The IR1 visa is much like the CR1 visa however your Thai wife will enter the US as an unconditional permanent resident. You wife can live and work indefinitely in the United States. You can only apply for an IR1 visa if you have been married for more than 2 years. You can use your Thai marriage registration papers for this when you apply for the visa. The application process for the IR-1 visa is about 12 months. This is about 4 months longer than a K3 visa process.
Note that for both the CR1 Visa and the IR1 Visa if you are a Resident of Thailand then you can apply at the USCIS offices in Bangkok which will save you at least 3 months on waiting on the application process.
You will note that you had to have registered your marriage in Thailand. The traditional ceremony will not count as your marriage date for these visas. Also note that plural marriages are illegal in Thailand and they also cannot be used for a CR1 or IR1 visa application.
Speak to an attorney about the visa process in Thailand and ensure that you meet the financial requirements of the visa as well as the visa medical checks and criminal record checks. If you are in doubt about the visa process then email for more information with regard to the visa process. If you have had a visa denial then check to see what the denial was based on an approach an immigration lawyer about the visa denial. These are normally very complex and needs an application for a waiver.