Hi Samia,
As for content for your direct mail piece make sure you have a strong headline to catch your reader's eye. Otherwise your potential customer may not realize you are "talking to him/her" and toss it. This should be followed by the benefits of using your services vs "Joe Movers". Direct mail also generally includes an offer for the recipient's reponse, whether it be a discount coupon for your services, or perhaps a free report on how to get ready for moving day. You can include in your mailing that if they call you they'll get the free report and the discount and then you could maybe do a little more "selling" over the phone by asking them if there is anything else you can help them with regarding their upcoming move. You can then follow up with all those that called you via phone or another mailing.
Also, have you considered approaching real estate agents? You could offer giving their referrals a discount. They are always looking for ways to "outshine" thier fellow agents and impress their clients. You could show them how relying on you to take care of their client's moving needs will enhance their reputation. Again...see how you point out the benefits?
These are just off the top of my head and hope they are helpful. Good luck.
Lea