For the WordPress side of things, to manually audit a WordPress’s sites speed on a server, to accurately identify the lagging culprit, I would
1) See if a basic php script is slow
make a test.php file with
<?php for ($i = 1; $i != 300; $i++) { echo "{$i}<br />"; } ?>
If that page takes a while and isn’t near instant, andor pingdom returns server response delays, your servers configured poorly andor your host is bad.
If not, continue
2) See if the database is slow
Do a basic php mysql test to your WordPress database, https://www.w3schools.com/php/php_mysql_connect.asp do something like read the table names
If that page isn’t instant, your mysql database is slow and needs some attention. If not, continue
3) See if its the third party WordPress plugins/themes are slow.
Disable all plugins and change theme to twenty-x theme. Load a page that has little no no inline images or videos. If site is still slow, it’s for sure the dedicated server, if its fast, then its a plugin or a theme slowing you down.
Add plugins back one-by-one, checking the load times until the sluggishness starts again. That’ll pinpoint the culprit. and lastly the theme.
(Additionally https://wordpress.org/plugins/query-monitor/ and https://github.com/Rarst/laps seem to be cool ways to see query and load times within WordPress)
Now, if it is just the dedicated server being slow, it’s (arguably) a lot of work maintaining, refining, optimizing, and securing. There’s hundreds of small things you can do to increase speed of your servers stack and have it running smoothly, along with setting up things to monitor resource stats and create notifications, etc. But being dedicated virtual, all that responsibility lands on you (and possibly you’re plesk/cpanel). Imho, its a lot of work and takes a lot of time.
The alternative to having to be part-time server admin, would be instead using somthing like GoDaddy has “Pro WordPress hosting” https://godaddy.com/hosting/pro-wordpress-hosting – I normally don’t support GD, but they’ve made the pricing really affordable, and they’ve setup the servers to be optimized for WordPress developers (and they do all the server work – giving you more time to focus on just WordPress). These environments are better than shared, and not as tedious as DV. Bluehost https://www.bluehost.com/products/wordpress-hosting and basically all the top dogs all have it as well.