I see now we're talking about apples vs. oranges here. This is NOT an IVP4 / IVP6 issue.
You said you could "log on" to the router…BUT
What you couldn't "get right" is the encryption between the router and the computer.
OS9 does NOT understand modern Wi-Fi encryption standards. The world currently uses WPA and/or WPA2 wireless encryption.
OS9 only understands WEP - a previous, less secure protocol.
You didn't say which model Apple base station you got - unless it's fairly new, you should be able to set it to WEP Wi-Fi which will work with OS9.
The less secure nature of that may be a concern…especially if you're in a dense metro area where a zillion folks can pick up your signal.
Realistically, this is not all that big of a deal since you're NOT going to be doing any banking or Medical or other vital stuff in OS9 anyway.
BUT, if you have any other devices on that Base Station, they will have to downgrade security as well and you may not want to go there.
Your powerline solution, as you've discovered, works also. There are also Ethernet-to-Wi-Fi bridge adapters that plug into the Ethernet jack and allow you to regain wireless connectivity while maintaining modern security.
So to recap, basically, it's the jump from computer to router that's the main issue.
You probably will run into a few website issues as you use OS9 where you can't speak their security language. You deal with those when and if.