Server Hardware Recommendations
Theatersoft is open source software that runs on local devices that you own and control. Your choose what device to use and decide what you connect to it and how you use it.
You can use any Linux hardware such as a Raspberry Pi 3 or mini PC, or a Linux container. If you want to run a sevice that requires access to a USB or PCIe device it could constrain your choice. E.g. a PCIe capture card would rule out a Pi3 or mini PC.
The Pi3 is inexpensive and commonly used in installation tutorials for this type of software. It’s a perfectly good choice to gain experience with Theatersoft installation. But it does have a few drawbacks including the questionable reliablity of a microSD card used for main storage. Plan to eventually use at least a mini PC if you want a faster and more reliable system. I’ll add more details to a followup post in the Devices and Hardware forum.
To securely access your client from outside your home network you will need to complete step 5 Configure dynamic DNS and server SSL certificate of the installation. That step requires you to have a domain name that you can point to your home IP address. If you need a domain name you can buy one for less than a dollar at Namecheap.