There are a lot of hosting providers out there, but when it comes to high performance webservers, most of them are just to basic.
The main difference in website hosting is shared hosting or a dedicated server (virtual or hardware).
Apache Solr is one of the most important peaces of software for a Drupal app with lots of content.
You can run Solr on a dedicated server of side by side with you LAMP stack.
To install Solr, first check which version of java is installed.