Of the engines you mention I've only worked with Elasticsearch and I'm quite happy with it.
To get started you could take a look at talk by Ben Corlett at Laracon 2014: https://murze.be/2015/01/using-elasticsearch-in-laravel/
Working with Elasticsearch in Laravel is easy with this package: https://github.com/freekmurze/searchindex
If you want to install elasticsearch on your dev machine or server you could follow these instructions on the Vaprobash repo: https://github.com/fideloper/Vaprobash/blob/master/scripts/elasticsearch.sh