Thank you candlebbq!

That information was fairly short compared to the volumes I've already been trying to write. Your answer was clear and makes sense!
We've ordered off newegg, but it was for just a 'regular' computer, not one tailored for gaming.
I am leaning towards the Asus G series, as I like the heat 'sources' are towards the back, instead of right under my hands. That's a pretty big deal for me. The only problem I'm seeing right now is they do tend to run pretty high. I think at Amazon the Asus G73 A1 comes w/ a backpack and mouse (bonus!)... but kind of on the pricier range.
Time will tell. I will continue to refer back to this information, as I'm about to 'throw out' the desktops! They take up too much room, but my children are already little gamers and will also need to learn 'information processing' here soon. I don't want their education to be as out-dated as mine.
If this gives you a clue... back when I was into working computers, Unix was the only system that was truly dual/multi-tasking at the same time!
~~CierraShore