You don't want to share your contact list to everyone - that would create endless problems with security you'd need to tighten up, they'd be able to see all your contacts and you'd manually have to add it as a shared folder.

To show the public folder in the Global Address List, you need to make sure it's mail enabled, which means it has an email address which can receive email. This should happen by default after you create it - to check, open Exchange System Manager, go to Administrative Groups, first administrative group (or whatever yours is called), Folders, Public Folders. Right-click the public folder, Properties, Email Addresses tab. If there is an email address there, it's mail enabled. If not, you'll need to close properties, right click the folder, all tasks, mail enable.

Once that's done, open the properties again, go to Exchange Advanced and untick "Hide from Exchange Address Lists". That will show it in the Global Address List (GAL), but if you've got Outlook 2003 in cached mode, you'll need to force it to update its copy of the Offline Address Book to see the changes. Alternatively, you can login to Outlook Web Access which uses a live copy of the address book which doesn't lag behind.

To force the Address book update, follow the instructions here: http://blogs.brnets.com/michael/archive/2005/04/26/512.aspx Then when you click To, CC or BCC, the name of your public folder should appear in the list and users can send to it.