The best thing to do is to not go wireless on the desktop, just put the router near it and connect the cable to the modem, the ethernet cable from modem to router, and another ethernet from router to desktop. It will be a slightly faster speed and it's not like the desktop's going anywhere.
If you're way the hell out in the middle of nowhere don't bother with securing the router unless you feel like it. If you're in a town, definitely read the manual for the router and secure it.
Don't get a linksys router, go with d-link or the one recommended above.
A 4-port wireless router has 4 outgoing ethernet cable ports plus the wireless thing. So not everything needs to be wireless, you'll have 4 ports if you need to wire things anyway. 802.11g is fastest but 802.11a is on a different frequency that might not interfere with cellphones. 802.11b seems to be standard.
If your laptops support g I'd go for a g-capable router.