Just to expand on what seatsd said, I've been using Norton System Works since '96; I've had very little trouble with it, but since coming here to DaniWeb I've learned quite a bit. Norton uses a lot more system resources than most other programs that do the same thing -- when my current subscription expires, I'm going to try something else. AVG is supposed to be one the better free antivirus programs, but, for a reasonable price, NOD32 is supposedly the best.
Don't ever let yourself be fooled into thinking you are fully protected -- it ain't gonna happen. The combination you described, a good AV, Spybot, and Ad-Aware will offer a good amount of protection; and you should consider adding SpywareBlaster as well. Keep everything updated, incuding Windows and IE! That's the most important thing. Most viruses, etc., are released after patches were made available to prevent them.
There shouldn't be any conflicts among anything you mentioned; is the firewall you're getting a hardware firewall or software firewall? If it's a software firewall, you should disable the Windows firewall or you will have conflicts there.
Using an alternative browser, such as Firefox, is a good idea, but you still need to keep IE as there will be a few sites that won't work with Firefox (Windows Update, in particular).
These threads may interest you as well:
http://www.daniweb.com/techtalkforums/thread16365.html
http://www.daniweb.com/techtalkforums/thread5690.html