We use the USPS (Post Office) direct mail and it works very well. You need to follow their criteria and you can find it on their website. If you need a good, very reasonable printer, try McCormack printing in Tipton (you can email everything to them).
We have used them for several mailings for our church. They do a good job and can handle everything, including taking the mailings to the Post Office. I'm pretty sure they can get every address or every address that isn't a business within a radius of an address.
Are you looking for a full 3-5 mile residential saturation (i.e., every household within 3-5 miles of a given location)? Is this a one-time project or something you want to do on a routine basis? Do you have an existing piece you want to distribute, or do you need help coming up with the design too?
Ask for Russ Bryant. They'll do it all. Obtain your targeted mailing list based on the specified demographics (or process your list), presort that list, print it, fold/tab or insert it, address it, package it, and deliver it to the BMAU downtown.
I used to work there. One stop shop. Most of the "marketing" places farm out the mail list services and postal processing to them.