For starters, being behind a router using NAT is very good for security (as opposed to just using a modem).
A few tips:
Choose a secure password, e.g., at least 12 long, with lowercase, uppercase and numbers. This is both for the router and your machine.
Disable access from the Internet to the router admin pages. Most routers won't allow it anyway, but just in case.
Set your wireless security to WPA or WPA2. If you only have WEP, you'll be better off not using wireless at all.
Ubuntu is pretty secure as it is, but for extra security in you own machine take a look at the several firewalls available (like UFW).
Hope it helps.