"Arigatou" is the correct romanization of ありがとう, which means "thank you". The way that you spelled it will also get your meaning across to others who know a bit of Japanese and the English alphabet.

"arigato" means "Thank you". About the spelling, To say more correctly, "arigatou" is normal. But, "arigato" is also OK. It's a bit casual way of saying. #Anyway, is it Ritsu(K-ON)? :)

Arigato(u) is one of the simplest way of expressing our gratitude. As satori0530 wrote above, to say "Arigato gozaimasu" is politer. I would recommend "Arigato gozaimasu", if you would visit Japan or talk to Japanese.

ありがとう= thanks, thank you (目下の人に対して使います。） ありがとうございます（目上の人に対して使います。）