If what you want is a quotation or offer, then sending a letter of intent makes you look ignorant while requesting a quotation will generally at least make you look like you know what it is that you want. And what you want, after all, is a price quote. Hence you want to request a price quote, via a request for quotation.
At the end you should sign off with "sincerely yours" or any other related salutation. If you are applying for a particular job then you need to create letter of intent that contains the following. First of all mention your name, address and contact number.