Make sure to close all tabs before closing Firefox or use Delete browsing, search and download history on Firefox to clear the history.

Thanks for the reply, but that is a "band-aid." I want the "restore previous session" box eliminated from my start page. No other search engine has that option, so I'm sure it is not impossible to obtain.

That is a feature of the new build-in Firefox Home page about:home
You can set anther page as your home page if you do not want to see that button, but that feature can still be accessed via Firefox > History > Restore Previous Session.

• How to set the home page

I appreciate your continuous diligence in finding a cure for my problem. I believe this will cure me!

You could use start a private browsing session when you go to sites you don't want others to know you visit. Firefox will not save your history during that session and will remember and restore only open tabs from before/after you start/stop the private browsing session.

I didn't want someone to be able to log into an email account such as gmail if I didn't specifically logout. This should solve your problem too.

Go to Tools -->Options-->Privacy tab. In the "Firefox will" drop down, select "Use custom settings for history". Then you probably want to deselect Permanent Private Browsing mode. However, the last option says "Clear history when Firefox closes" you want to check that and modify this option by hitting the Settings button. You likely do not want to delete all Cookies every time you close Firefox but you do want it to delete History (and perhaps Form entries and Cache).