The Zulip server uses very little CPU, but the RAM is important. (I work on Zulip.)
Here's what the docs say, for reference (excerpt of https://zulip.readthedocs.io/en/latest/production/maintain-s... ):
> For an organization with 100+ users, it’s important to have more than 4GB of RAM on the system. Zulip will install on a system with 2GB of RAM, but with less than 3.5GB of RAM, it will run its queue processors multithreaded to conserve memory; this creates a significant performance bottleneck.
> chat.zulip.org, with thousands of user accounts and thousands of messages sent every week, has 8GB of RAM, 4 cores, and 80GB of disk. The CPUs are essentially always idle, but the 8GB of RAM is important.
As a practical matter, I think 4GB of RAM is not a lot to ask for a service that 100+ users are actually concurrently using all day. That's a small fraction of the RAM the clients are consuming; and you can get a suitable cloud machine from Digital Ocean (simpler pricing than AWS, so good for a quick price check) for $20 USD/mo.
On the implementation side, it turns out that a lot of moving parts go into a full-featured chat app. Here's a partial architecture diagram, plus detailed exposition:
https://zulip.readthedocs.io/en/latest/overview/architecture...
Database, plus caches, plus code for lots of features x running in a number of processes, adds up to a few gigs of memory.