If you have a decent router and at least DSL, it shouldn't take too long at all to connect to the Wii Shop. You just have to remember to go into the Wii Settings and update the firmware. You also have to make sure the Wii has successfully connected to and tested connection with the router in order for it to automatically connect to the Internet and stay connected through WiiConnect24.
These steps, however, should have been completed upon first turning the Wii power on. If you skipped them, you can return to the Wii Settings menu and go through the various steps one-at-a-time.