Buyer accepts offer and signs it, where offer acceptance is binding depends of the legal jurisdiction. For example English and common law differs slightly from American uniform commercial law on matters of offer acceptance and when performance becomes binding on an offer. The seller can also reply with a pro forma invoice. In fact a pro forma invoice can serve as quote and offer, becoming a more or less binding purchase order upon buyer acceptance and signing. Pro formas are used more in smaller FCL trades, and not in larger bulk trades.
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.