Selfhosted

If you're proficient it's 30minutes

Something like this for server.

generate config

docker run -it --rm \
    -v <your-data-path>:/data \
    -e SYNAPSE_SERVER_NAME=<your-public-address-subdomain> \
    -e SYNAPSE_REPORT_STATS=no \
    matrixdotorg/synapse:v1.136.0 generate

run

docker run -d \
  --restart=always \
  --name synapse \
  -e SYNAPSE_REPORT_STATS=no \
  -v <your-data-path>:/data \
  -p 8008:8008 matrixdotorg/synapse:v1.136.0

register user

docker exec -ti synapse register_new_matrix_user http://localhost:8008/ -c /data/homeserver.yaml -u <username> -p <password> --exists-ok

Proxy it using ex. openresty / nginx

location / {
        proxy_pass    http://127.0.0.1:8008/;
        proxy_http_version 1.1;
        proxy_set_header    Upgrade         $http_upgrade;
        proxy_set_header    Connection      "upgrade";
        proxy_set_header    Host            $host;
        proxy_set_header    X-Real-IP       $remote_addr;
        proxy_set_header    X-Forwarded-for $remote_addr;
        proxy_connect_timeout 600;
        proxy_read_timeout 86400;
    }

For UI if you want element on your domain, download and unpack tar.gz from.
https://github.com/element-hq/element-web/releases

Point this location to your proxy server ex. openresty / nginx

location / {
        root /opt/element-v1.11.109;
        index index.html;
    }

Modify config.json inside /opt/element-v1.11.109 to point location to <your-public-address-subdomain>

By default it's using sqlite if you want postgres or other database then modify homeserver.yaml to use postgres