Hi Montree, for more new tab page options, you can use an add-on to assign the page. This is the usual recommendation:

https://addons.mozilla.org/firefox/addon/new-tab-override/

Can you get it working with the Google home page?

Now... to be logged in automatically, you'll want to avoid clearing your Google cookies between sessions. That way, you'll stay logged in continuously (until you log out).

You can use these steps to make a website recognize and remember you.

• create a cookie allow exception with the proper protocol (https:// or http://) to make a website remember you

You can check that you aren't clearing important cookies.

• using "Delete cookies and site data when Firefox is closed" keeps cookies with an allow exception
• using "Clear history when Firefox closes" to clear cookies clears all cookies including cookies with an allow exception you may want to keep
• clearing "Site Preferences" clears exceptions for cookies, images, pop-up windows, and software installation and exceptions for passwords and other website specific data

• Settings -> Privacy & Security
  Cookies and Site Data: "Manage Exceptions"