Let me say that I see no virtue at all in the new Search Box arrangement.

A quick thing you may not have tried. Enter your search term first(before you select the search engine). Then "Enter" will search via the default search engine. If you want to use a different search engine then hover next to the magnifying glass and the small, revealed down arrow will take you to your other search engines.

I don't understand why the down arrow is not always visible. Maybe it is on other computers.

In the address bar, type about:preferences#search<enter>

If you miss being able to switch search engines without going crazy with menus, try this out;

Context Search {web link} Expands the context menu's 'Search for' item into a list of installed search engines, allowing you to choose the engine you want to use for each search.

Just for the record FredMcD , I totally support your recommendation of Context Search to use with items selected on web pages. I use it 90% of the time.

A great time saver.

You can revert to the previous search bar scheme by changing one hidden preference.

Open up about:config (typed in the Location Bar) and toggle this preference to false

browser.search.showOneOffButtons

Then restart Firefox.