I'm not a lawyer, but... (and recognize that a lawyer isn't even necessary, though would be highly advisable.)
An offer letter should clearly present the elements of your offer: It should specify the property address (both the common address and the legal--such as lot and square--address). It should specify the amount you're offering. It should specify any conditions you're attaching to the offer--for instance, subject to a home inspection, and/or subject to your finding acceptable (to you) financing. Beyond the issue of a home inspection, it should specify whether you are buying the house in "as is" condition, or whether you require any repairs to be made. It should specify a time frame by which the transaction must be completed. It should specify who the purchaser is/purchasers are, and should identify all sellers. There's more to it than that, ideally, but all you need for a legal contract (again, I'm not a lawyer) is a written agreement identifying what is to be sold and for how much. There should also be "consideration"--which in your case would be termed "valuable consideration"--which can be as little as $1. Also, either have a lawyer review what you send before you send it, or include a contingency: "This agreement is subject to the approval of buyer's legal counsel."
Feel free to contact me; I've got some 1-page and 2-page offer letters that investors use when dealing directly with sellers.