How do I get thunderbird to give notifications for only my inbox

Starting with Oneiric, the Thunderbird version shipped with Ubuntu has an add-on bundled that handles integration into the message menu. That add-on called "Message menu and Unitiy Launcher integration" provides some additional options on the General tab in your Thunderbird settings (not sure about the wording, as I'm re-translating from German here ;) ). Near the options to play a sound file when a new mail arrives and such, you can decide whether the message notification should be lit for new mails and whether to do that for every folder or just for the inbox. I don't know a solution for choosing a custom set of folders, but maybe there's an add-on out there to do that.

TL;DR

Edit > Preferences > When new messages arrive > checkbox "Show in the messaging menu" > change radio from "For messages in all folders" to "Only for messages in my Inbox folder"

The Mailbox Alert let's you display different notifications and play sounds on different folders. Even on search folders.

Download

Set up

There is a bug in the add-on launchpad asking for that kind of feature. At this time, as Henning wrote, or all email or just inbox folders. All email includes RSS feeds :(