I actually had a similar issue. I went to a thrift store to buy an old router, paid $3 for one, got it home, found out that it was a really old one with no wireless support. Then I found the one I'm currently using at an estate sale.
Once you actually get the router working, getting onto the private server is easy. All it requires is a DNS change. Besides Mario Kart, what online games do you have? I have Mario Kart, Warioware DIY, a few Pokemon games, and some other random games that no one ever plays online.