I'm looking at buying this HP desktop and I think everything in it would be able to play TS3, as well as other games, really good. Someone on Yahoo Answers suggested I swap out the default AMD 7450 graphics card to the Nvidia GeForce GT640, because that would be able to play games more smoothly on higher graphics settings, but I don't know much about computers. The specs for this desktop are this:

Operating system Windows 7 Home Premium [64-bit]
Processor AMD FX-6120 six-core processor [3.6GHz, 6MB L2/8MB L3 Cache]
Memory 6GB DDR3-1600MHz SDRAM [2 DIMMs]
Hard drive 1TB 7200 rpm SATA hard drive
Graphics card 1GB AMD HD 7450 [HDMI, DVI, VGA adapter] OR 3GB Nvidia GeForce GT640 [DVI, HDMI and VGA via adapter]
Power Supply 300W Power supply OR 460W Power supply

Should I upgrade the graphics card to the 640, keep it at the 7450, or what? Any other suggestions? I want to play several other large, new games on this computer as well as TS3 and I don't want to waste a bunch of money on something that doesn't meet my needs.

What size monitor and screen resolution do you play on?
If it were me, neither. Newer DX11 games released this year and next would choke on those cards on high resolution.
Have you check those cards in the Wiki? What colors do they have? If the are too new that there's no record for the particular model, the older series is always a good indicator on how they perform. So, in summary, good cards are those in Green across the board. Colorful ones won't be able to handle "large, new games", if you want nice graphics and high-enough FPS to not lag.

What's your budget? HP does offer better cards but they look a tad more expensive than those offered in online sites. EG: HP's 7770 2GB is $230.00 versus newegg's @ $160

Well, right now I don't play AT ALL because my current laptop can't even play TS2, so I KNOW it can't play TS3. Newer games would choke? As in, not be able to play?

I checked the wiki, but these cards are too new to be on it, I guess. My budget is pretty tight, the computer I linked to would be incredibly expensive for me.