if you go to the homepage, you\'ll see that before the page loads, the browser waits ...
How i could reduce Time for the first byte?
The delay is caused by the server-side script which generates the index page.
By a quick look at your website, I can guess that the website is using PHP. So, the delay is caused by something contained in your index.php script.
The hosting, the network, the hardware and the HTTP server (Apache) are definitely NOT the cause. Your graph shows that static files (.css, .js and so on) are delivered rather fast.
So, for more details you should provide more information (the slow execution of index.php can have many different reasons...).