This is an overview of the main points that came out of discussions about how the home and app tabs should appear:

Home Tab

On the home tab all normal browser chrome is hidden.
The home page has a location bar at the top of the window where it would normally be if chrome was visible.
The main content of the home tab is the Google logo and search box (or alternative depending on the locale).
The home tab is always present at the left of all other tabs on all windows for the user to go to.
Navigating to any new page from the home tab opens a new tab.
When the user goes back to the home tab they should see an empty search box and location bar.
If there is search engine selection on the home tab it should forget the selected engine when the user goes back to the tab

App Tabs

App tabs appear to the right of the home tab before all normal tabs.
App tabs appear on every window.
App tabs always restore on startup.
App tabs may display less chrome, or have options to do so (none, minimal or all). The default may come from the web-app.
Navigating to a new domain opens a new normal tab.
Dragging tabs to the home tab turns them into an app tab. Some kind of clever threshold will be needed to tell whether the user wanted an app-tab or just to move to the first tab.
Normal tabs have a context menu item to convert it to an App tab.
App tabs have a context menu to allow, among other things, removing an App tab.
Need to consider whether Cmd-W on an app tab does nothing or closes the entire window losing everything from app tabs.
In new windows app tabs don't load their content until they are viewed (BarTab-like functionality). The initial state may look visually different to differentiate the two states.

Note: This has implications for TabCandy, since you're more likely to activate an app tab than to move to the group it's in.

If the user just had the default Firefox start page as their home page then just display the home tab. Otherwise display an app tab with chrome enabled for their home page as well as the home tab.
The bookmarks toolbar will be turned off if the user only have the default bookmarks.