You can add the Google search to a new tab page with an extension, appropriately named Add Google search to new tab page

You can modify the browser.newtab.url pref on the about:config page and set its value to your preferred new tab page.

• http://kb.mozillazine.org/about:config

cor-el, your detailed answer was great! Providing the exact item in the list of hundreds/thousands narrowed it down perfectly.

Note to others, I turned off the showing of all the recent sites (very few I visit often enough to be given that list on each new tab, history and multiple tabs does what I need).

You toggle them on/off with the only icon in the upper right of the page (looks like floor tiles with space between each tile) and even when turned off the selected browser.newtab.url shows.