I self-hosted it few months ago, and it's actually surprisingly easy! Someone has made an Ansible script for Matrix with Element and some bridges, that (at least a month ago, IaaC tends to be pretty fragile) worked out of the box on a first try. I just set up some config values (mostly about enabling bridges I want) based on their amazing documentation, and then ran it once and everything is working so far. I even updated it several times already, and every time it was smooth, and it was basically just running a single ansible command. Their documentation is pretty well written, and with my basic cloud, IT and Linux knowledge I had no issues with following it. All you need to know is how to set up cloud VM, get a domain and set DNS, and set up SSH keys to access the server.
In total it took me about two hours in total, from when I decided "I'm setting up Matrix tonight" without any prior knowledge, looking up my options and finding the ansible script, setting up cloud and getting Matrix up and running.
I'm renting a VM on Hetzner for like 6$ per month, and it worked without issues so far. I use it for Discord and Messenger, although the Meta bridge does have some problems, for example I didn't figure out how to message someone with whom I haven't had a conversation since I set up the bridge, since only then it creates the room for it. But that can be solved by keeping the Messenger app or usign the browser to send a first message, and it immediately shows in your Matrix bridge (and stays there forever).