I did all mine through the US embassy in Bangkok by mail. They have a complete list of required actions and procedures. Since you are sending your original passport to the embassy by mail make sure you make copies of your passport.
There is a document for Thai immigration for transfer of the stamp. There is a document the US embassy will provide you asking for the Thai immigration to transfer. Take your old passport and new passport.
I found a Kodak photo shop in a small alley in Patong Beach for my new passport photos. 2 excellent quality prints for 100 baht. Not familiar with your area but most print shops also do passport photos. When I was looking for a place to print my documents to sign and prepare for mailing is how I found my photo location.
for the passport application it is online payment. The item you get a 100 baht check from the bank is to cover the registered Thai mail of your passport back to you inside Thailand. There is a form on the embassy website that you would need to print and take with you to one of the 3 specific banks with instructions.
You mail your current passport along with the application and check from one of 3 Thai banks to cover the return postage inside Thailand. The US embassy will mail your passport application back to the US for processing and minimum time is 3 weeks.