Ping cannot be too low.

Yes... your router certainly is weird.
I would recommend a DMZ Server at this point, since it simply opens all ports to a specific IP.

I suppose this might still be a problem, I assume you can't open all the ports because it give you a conflict message?

Here's the thing.... it sounds somewhat like your router needs ports to simply function, which is kind of strange.
At least allocated ports...
Eh, you might just be screwed, sorry.

Original IP is the default IP address of your router.
It can be found in the IPconfig menu of your computer.

Hmm...
Glad to see you could at least log in.
Most routers have in-depth guides posted on www.portforward.com.
Sadly, it seems your Router is either very new or a type not many people have, because it is not listed there.

As for Forwarding vs Triggering.
Yes, you generally need to use the customizable slots for forwarding, not triggering.

SPI firewall truthfully is much less important than simply opening the ports for the Wii.

The other option to forwarding is to create a Default DMZ server, which is basically the same thing as port forwarding except it opens every port to the specified IP. Some routers have this option under its own category, or bundled with other wireless settings.

However, if you can get the Wii to run through the the specific ports in this guide, don't fool with a DMZ Server.
All I can really do now is advise you attempt putting in the ports anywhere they can be entered, be it forwarding or triggering, and see if the Wii will connect to the internet. If it doesn't work, simply reset the Wii's original setting before you switched and try something else. Some routers make it needlessly cumbersome to do something like this, but just know that if you do get it to work it will be worth it.