About a week and a half ago, I dropped letters in my clients' target neighborhood. It is a community of less than 100 homes. I received two responses and showed both properties to my client.
The key to anything you do is authenticity. If you need a loan, be pre-approved for one prior to dropping the letters and be prepared to pay market value. In addition to those items, your letter should outline the features you want in a home, what you're flexible on as well as any "must haves".
Homeowners receive pitch letters all the time from liar Realtors who don't actually have a buyer for their home, so homeowners are rightly skeptical. Homeowners will question you. Best practice is to be open and answer their questions.
I don't know how homeowners will react to an individual dropping letters saying they want to purchase their home. Safety is the first thing that comes to mind. People may think you want access to their home to harm or steal from them.
Again, authenticity is the key. Provide information about yourself or enlist the assistance of a Realtor to draft, print and drop the letters, receive inquiries and arrange for showings should you receive any responses.
Importantly and so much unlike this response, keep it concise.
Homeowners receive a lot of mailings soliciting their listings, telling them about neighborhood sales, offering free market analyses - they get a lot of mail. They are not likely to sell just because they receive an offer in the mail.
All the best,