Ah, I see. Competitive battling takes a lot of work and dedication, so if you think you're up to the task, you've got my respect.
The Wii can use multiple kinds of "wi-fi", so it's usually compatible with routers. The DS is a lot more limited, sadly. So you'll probably need to buy a DS-compatible router, in short. Just like me; except I won't be coughing up money any time soon. I have to put up with my Wi-fi USB Adapter... it's a piece of junk. -.-;