How to update Debian, ISPmanager and PHP for WP site?

Question

Debian

Good day everyone!
I have a WP site that takes a long time to load. There are problems both client, and server. For example, a very high First Byte (1.5 sec.) and Start Render (3.2 sec.), although it is on a dedicated server.
Information about the site:
1. Works on the old theme, which is already several. has not been updated for years.
2. Works on PHP5 and legacy OS.
3. Located on a dedicated server with IPSmanager4.
4. The site has pages and widgets that were completed by the programmer.
There is a desire to both update the design and speed up the loading of the site. We think that this will most likely require updating the theme, updating the OS on the server, updating the PHP5 version. Plus, we want to switch to HTTPS. But how to do all this in the correct sequence and as quickly / safely as possible?
The site receives traffic and should run smoothly.
The support service advises you to switch to a new server with an updated OS and ISPmanager 5 Lite. Then, supposedly, you can transfer the site through the built-in migration function.
When asked whether it is possible to upgrade the OS on an existing server, they say that ISPmanager 4 only allows upgrading to Debian 7, so it's better to move to a new server with ISPmanager 5 Lite.
That is, it is not a fact that after the transfer the site will work correctly on an updated server, PHP ... And it is not a fact that it will load faster on a new server. Maybe changing the template will help speed up? But in this case, everything can limp ...
What can you advise?
PS I'm such a layman in development and server business that for me PHP and Node.JS are all the same. I would be glad to receive constructive and useful advice.

Answer 1

1) Do not touch production. Let it work normally.
2) We create a local copy of the site or a copy of the site on the server and be sure to close it from indexing. You can even password-protect via htaccess & htpasswd
3) Turn on PHP version 7.0 and higher, finalize the site, update plugins, themes, fix bugs
4) Take a new server with LAMP + ISP Manager 5 or Vesta. (for example, Debian Stretch)
5) Set up a new server and transfer the site
6) turn on the debug and finally check the site.
7) If everything is OK, then we change the DNS records so that the domain points to the new server.
See what they advise you on the site
https://gtmetrix.com/
https://developers.google.com/speed/pagespeed/insights/
There can be many reasons ... You need to study first. These are server resources, and server configuration, and the VP site itself, etc. It will also help to connect a CDN service and upload static files from cookie-free domains or from a site subdomain.