I am running a similar setup at home. The LAN cable should go to the wireless router, then if you make sure you get a router with switch you can easily connect your desktop machine with cable and use wireless for the laptop.
Regarding security, there are several options.
Hidden SSID will make your network invisible to normal scans. This should be combined with some sort of encryption to make it safe.
WEP encryption is the oldest and weakest form, but also the best for backwards compatability
WPA is a better encryption and would be my suggestion, either that or
WPA2 if you buy a router that supports this. (And make sure your networkcard also supports it)
The encryption is quite easy to set up, using WPA or WPA2, you simply choose a passkey, that you then enter on your computer to connect.
I am using a Sanberg Wireless G54, which works without problems. If you want to go a step up, you never go wrong with a 3Com or LinkSys device.
Good luck.