A router is a lot better tho. It can be 24/7 on, and has a lot more range. Router's price may vary depending the model, some of the good ones are from 40$-70$. I would suggest the "Linksys" series of routers, since most of them are compatible with the Wii and the DS.
You don't need to connect anything to the DS to use Wi-Fi. If the wireless router's compatible, your Wi-Fi game should be able to connect. The DS has a built in connector.