In order to optimize a shared server for Joomla you have to decrease the load your site puts on the server.
There are several ways you can do this.
This step is for new Joomla users. If you are just starting out delete ALL files out of the directory you are going to use. Joomla will install necessary files to secure your site (.htaccess file).
On this same token, it's never good to have multiple websites running on the same cPanel area. It gets cluttered and requires more resources to be dedicated to accessing files deep within directories.
If you are moving Joomla or doing a major upgrade to the site, move it to another server temporarily and delete out the old database. Create a new one and then copy your files back onto it. *Be careful not to delete the database until you have it backed up
When it comes to speed, shared servers show their true colors when they have to retrieve an image. Using a Content Delivery Network takes the load off your shared server by serving up the image for you.
Files like .HTML, .CSS and .JS files can usually be compressed (minified) into a much smaller version of the same file by taking out spacing and comments left in their for us humans to read. Computers only need data, so it makes the files much smaller when they are brought down in size.
Combining files is more difficult because it risks breaking documents. Try to get it to work, but in some cases it can be more trouble than it's worth.
Contact us if you have any other suggestions!