LOL.  -I've had doubts as to where to post something too.

I'm no expert, but we should start with what kind of video card you have, or plan to acquire.  Does it have dual video outputs, meaning can you physically plug in two monitors to it? 

Video card wise I have the capability to do so.  It is an EVGA 8800 GTS with dual video outputs.  The only hold back on running a dual monitor setup is more of a spousal issue.  My wife is very intelligent and where I can slip a new video card or memory, etc by her, a second monitor will be hard to hide.  Guess I could put a house plant in front of it, but that would kind of defeat the purpose.  If there is no advantage to running dual monitors and it does not help my problem then I would not fool with devising a sales pitch for her.

I run two monitors. I have a nice big one for my primary, and a smaller one for my secondary. i keep the start bar and all my icons and such in the secondary. however, since it is actually set up as #1 and #2, everything that opens goes to #1 by default. things will only go for #2 if ive moved them there and they can remember window locations (things like chat, itunes, firefox, etc).

as far as a virus alert popping up, the only thing you can really do is either run all your fullscreen games in windowed mode or turn off the alerts. if youre running a virus scan while gaming, youll get lagged anyway cause your processor is split between functions. but yeah, since TF2 runs fullscreen by default, any new window opening that has the little "when this opens, it opens in front of everythign else," will just rip you out of full screen like you just alt-tabbed.

as for justifying a second monitor, this can be trickier. For me, i use dual screens for my creative stuff (photoshop, blender, etc). the extra real estate gives me a shit ton of more space to work with, and jsut makes life easier overall. but if you arent doing this, it could be a lot harder to justify. also i have a lot of friends who are computer science majors and they can't live without dual (or more...) monitors. just look at sirus' set up. he has somethign like 5 screens all in a row for all his shenanigans.

and why would the wife not want you to have a second monitor anyway?

Get rid of the anti-virus software you're using and get Kaspersky.  I also had similar headaches when I had Norton.  Kasperky has the ability to be run only when it isn't interfering with other apps.  It will actually shut down temporarily if I start doing something while it's scanning, then restart when I'm done.  It also found about 12 pieces of poison on my rig that Norton AND McAffee didn't detect.   I understand it's developed in  Eastern Europe (Russia)  which is where a lot of these viruses are being written.  Probably the same guys writing code for both!

i run TF2 in a window, i have a large enough screen to where it barely affects my ability to see the game.

Getting dual monitors to work the way you want in Windows is very tricky. I would almost suggest learning Linux and using Crossover to play TF2, allowing you to run separate Xserver instances on each screen, while also negating the need for virus/malware scanning. But that's a lot of work, and probably more trouble than it's worth.

Here's the best answer I can give; in Windows, if you use the nVidia DualView option, which allows you to have one desktop per monitor, notifications and alerts will always pop up on the primary display, and fullscreen applications will default to the primary display as well. You can purchase applications that will duplicate the task bar on the second monitor, and you can certainly move individual windows to the second monitor, but Windows does not have the ability to set the default display for most applications. If you are running software in the background that has a tendency to interrupt your fullscreen applications on a single display, switching to dual displays will not solve your problem.

I myself have dual monitors, and I really only use them for keeping web pages open on the second display while playing games or watching movies, and it is sometimes helpful for programming.