arigatou - "thanks"
doumo - "thanks"
arigatou gozaimasu - "thank you"
doumo arigatou - same as arigatou, but more emphasis - "thanks so much"
doumo arigatou gozaimasu - "thank you very much"
"Doumo" can be closer to a polite "thank you," too, said in the right place. Of course the word has other meanings as well, so I advise sticking it in a "thanks' expression of gratitude for now...