You didn't add much context. So I'm in the position I have to assume things. I assume your customer is a company and it's your company speaking.
"Thank you for your order! We look forward to doing business with you!"
I would write this:
Vi ringraziamo per il Vostro gradito ordine. Speriamo questo sia l'inizio di una proficua collaborazione tra le nostre società.
Of course there are many different formulas you can use, but generally Italian commercial letters are not warm, actually they are pretty cold, we never use exclamations marks, they might be used in advertising only to give more emphasis, on the other hand advertising is usually informal and not formal like business letters.