There isn't any built-in feature like that, but you might be able to use an add-on or custom style rule to reposition the top row (typically refers to searching or to visiting the autofill site in the address bar) to the end. Firefox 46 has a new address bar drop-down design compared with Firefox 43-47 and earlier versions, so the ease/difficulty may depend on which version you are using, and whether you already use any add-ons that modify the design.

Does pressing the down arrow select Google?

It does for me with Firefox 43 thru 48 search bar, with Yahoo left as the default search engine.

As far as re-postioning search engines in the listing, the 8 'provided' search engines seem to be stuck where they are. I didn't find a way to re-arrange them, but was able to "position" any added search engine based upon the order that they were installed. IOW, last installed was at the bottom of the list.

But, I hate the new search bar scheme and use this extension to get the old searchbat scheme back. https://addons.mozilla.org/en-US/firefox/addon/old-search-fixed2/