All our sites are running on WordPress, the largest CMS (Content Management System) on the Internet today. We are running most of our sites in a couple of different Multisites (for our internal sites, for our external clients, for development/staging).
We are using DigitalOcean's VPSs (Virtual Private Servers) to host our web sites. They are located in Holland for best possible access times in Europe. We are usually using a droplet with 1 GB RAM, 1 Core processor, 30 GB SSD disk. On that we can run 2 or 3 Multisites depending on the number of subsites (usually 5-10).
We run Ubuntu LTS as our operating system.
To handle the stack (the programs running a web server) we use the Coach plan on ServerPilot.io. I also gives us supervision of the CPU, memory and hard disk space. It installs (2018) among other things PHP 5.4-7.2, Apache, Nginx, and MySQL. It also handles our SSL certificate for the https protocol.
A fantastic set of plugins to setup Custom Post Types, Maps, Views, and Layout for WordPress.
The more we use it, the more impressed we are with the flexibility and stability.
A few examples from this site
StudioPress makes their own child themes for the Genesis framework.
We also have themes from Imagely. We use one of them here at adolfsson.photo (Expedition with a lot of tweaking with Toolset).
Some of the links above are affiliate links so if you buy through them, we get a small commission, thanks.