There are various types of letters of intents for instance if you are applying for university or college then you would need to create a letter of intent for graduate school or university. If you are planning to apply for a job then you would need a letter of intent for a particular job position.
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.