Unfortunately, you can do everything right and still not be able to connect, as modern DNSSEC sees the DNS redirection that private servers do as a malicious man-in-the-middle DNS attack. As DNSSEC rolls out more, chances are changing the DNS server will work for nobody as ISP routing will always override by using an authoritative DNS server.
If you set everything up right and still get Error 102 immediately (if you hang on the "Connecting to DNS server" screen, you need to check your set up), you can get around this by using an Action Replay code to change the server that PSO requests.
https://ragol.org/schtserv
Above is a full list of AR codes for SCHTServ for all versions of the GameCube game. They should always work providing SCHTServ doesn't change its DNS server address.
Set your DNS and IP in-game to automatic, set it in Dolphin's settings to 8.8.8.8 if using Dolphin, and use an AR code above as for your version, and you will be able to connect.