OK, first things first: the only 100% secure computer is one that you never switch on and use. That doesn't mean you cannot aim for 99.9% though
Most up to date Internet security suites and anti-virus solutions do now include rootkit scanning in some form or other. All you really need to know about a rootkit, if you don't want to get lost in the technicality, is that one can be used to hide malicious software from the OS.
Getting someone's IP address is very easy indeed. Whether you want to keep yours secret at all costs depends upon how paranoid you are.
There are better firewalls out there than ZoneAlarm Free, for sure, but everyone will recommend something different. The truth of the matter is that provided you have the basic protection in place, and an Internet secuirty suite is good enough (I am Contributing Editor of PC Pro magazine in the UK, and our current recommended security suite is Norton 360 which performed well in our tests - I use it here on one of my Vista machines and have no problems with it), then good security boils down to what you do with your computer.
If you practise safe hex, do not link click on anything that arrives unsolicited in email, do not download dodgy free software, do not install porn movie viewers, do not fall for the too good to be true scams that plague the Internet, then you should stay fairly safe.