I have a preliminary implementation of an entirely static build of Myths on Maps, here.
It uses OpenLayers and the tomik23 autocomplete javascript libraries.
I chose the tomik23 autocomplete for the option set but especially performance. It was also the only lib that could handle a large JSON data set.
I looked at:
https://github.com/TarekRaafat/autoComplete.js - too slow, docs decent, but lacked enough detail to use quickly
https://goodies.pixabay.com/javascript/auto-complete/demo.html - good, but too slow
https://github.com/alphagov/accessible-autocomplete - too slow