LAN Adaptor = wired connection, which makes a difference from your Wii to your router (some claim wired connections are superior, but I'd imagine how much so depends on the location). From there, DSL is DSL.
Though, if your router has the option to assign an IP address as a "demilitarized zone" (DMZ), do that for your Wii. You don't want to do that with computers since it disables all of the router's protections for that IP, but the odds of your Wii getting anything malicious sent to it through the internet are pretty much nill.
Also, as mentioned earlier, there is more to lag than your own connection speed. If the game server is bogged down due to traffic, you're screwed no matter what your connection is.
Also on DeviantArt, Rumble, DLive.tv, and the Fediverse (@freespeechextremist.com and @bae.st)