Is there any advantage to doing the static IP thing over DHCP? Is it a security issue? How do you do the static IP thing, do you have to manually enter the ip address every time you connect? I'm clueless when it comes to these things, and ironically my daughter just bought and hooked a router yesterday, first one we've ever had. I'm a little nervous about the whole security thing! How do I know for sure my network is secure? Lot of questions, eh?
Sorry, OP, since your question has been answered, I'm gonna thread hijack.
Static IP provides almost no security benefit over DHCP, aside for the afforementioned needing to know your router settings (which are common across the board, and easy to guess).
Basic router security is simple: password protection with WPA or WPA2. WEP is the old standard, and easily cracked by anyone with 15 minutes and commitment. I could teach anyone with a laptop how to break WEP in less time than it would take me to mow my backyard.
WPA and WPA2 are not unbreakable, but significantly harder to break than WEP, and are the preferred home security standards for wireless. I use WPA2 only, and barring my neighbor being an evil mastermind, I have no fear.
If you're really really paranoid, you can allow only specific devices to connect to your network using a MAC filter. This is again, not unbreakable, but a good level of security. I find it completely useless, and more of a headache than it's worth, considering how often new devices come on my network.
Just password protect the thing, and you'll be fine.