As srobarts says, broadcasting SSID (the name of the router/network) means the wireless router announces its presence: if you look at the wireless networks within range, it will be listed there. If SSID is not broadcast, the wireless router doesn't announce its presence, but still accepts connections. In other words, you need to know it's there. And, of course, you need to know how to enter the connection details
I'd be tempted to leave SSID on for your convenience, but consider filtering by MAC address (the network card's serial number). Also, and I realise this is not fashionable but it's easy to do, change the password more than once a decade.
(I don't broadcast, MAC filter, have a router that does new passwords every 2 hours for new sessions. But I'm a dork. I have a separate AOSS router for the Wii and DSi. AOSS is a great idea.)
Avoiding WEP: In the real world, why bother? No-one is going to hack your network to hack you. They're going to do it for some other reason. (Having said that, I don't use WEP myself)