How do I change what songs play after I play a searched song from my library

Click the magnifying glass in the search box and make sure that Search Entire Library is not ticked. When you search for something to play the view should narrow down to your selection. If you can make it match the one song then that should be all that plays. Otherwise tap the hamburger menu to the right of the notification area at the top of the iTunes windows and tap clear to remove tracks from the queue.

tt2

I don't think you can do it quite like that. What you can do is start a playlist off, then get a particular track to play next, after which you should go back to the original list.

tt2