That's a great idea to post your facebook fan page in your thank you note! That should get you some true fans.
I set up my Fan Page a couple years ago and got the bulk of my "fans" in that initial stage. Make sure you send out an announcement from your personal site that you are so excited to be sharing the launch of your facebook fan page, provide the link, let them know you will be offering exclusive info and discounts and to please spread the word. I've received a lot of true fans from friends of friends or friends of fans.
Also, you fan page is public, so the more activity you get (people liking, commenting, and posting on your page) the more likely it is to make it to the wall for everyone to see. I've had completely random people from other parts of the world discover me that way.
In terms of continuing to promote your fan page- I have seen many business to special offers to increase fans. Like whoever gets the most people to like my page wins a free "_____". Or Set a goal of how many fans you want in a certain period of time, and then randomly pick a winner. I have also seen people ask their fans to comment on their favorite item by you, post the link in their comment. That get traffic to your site, and then you randomly choose a winner to get a free gift. Just some ideas I have seen going around.
@lewisandbucky- yes, you cannot friend on your fan page, but you can "like". That is important because is creates your own profile and lets your customers in on who you are.
Hope this helps!
