An old friend of mine got me back on the Project M hype train. If you didn't know, Project M is essentially Super Smash Bros. Brawl with the mechanics from Melee. You can either run it in Dolphin, or on a Wii, but it's actually way better in Dolphin. You get better resolution, graphics, and even fast almost lagless play over the internet. I've been playing almost every day against a friend in Seattle and most of the time you could never tell it's online.
If you want to set it up, just follow this guide.
After that's all setup, I'd recommend you adjust your internal resolution. You can do this by opening the Graphics settings:
Try to play around with it and see what resolutions you can run without lagging.
If you're like me, you're probably only ever used to playing Smash on a gamecube controller. You can actually setup Dolphin to use Gamecube controllers as well. You just need an adapter and controllers. Probably the best adapters are either the Mayflash adapter or the official Wii U adapter.
Unless you already have an official one, I'd recommend the Mayflash one, simply because Official Gamecube and Smash related stuff has become fairly overpriced.
The setup for the adapter can be found here.
The instructions for setting up Netplay can also be found at the initial guide. You just need to send your friend your host code, and they should be able to connect without issue.
Project M also supports local play, so you can use it instead of your old Wii and get even better resolution. Just make sure to setup your additional controller ports and hit play.