@MixedMag Your system should absolutely be able to handle everything TS3 can throw at it. But there are other causes of the graphics glitches you've described. First, when you loaded the game, did you change the preset graphics options at the Main Menu and then immediately load a town? Adjusting certain settings without quitting to desktop and reloading can definitely cause this problem.
The fix is easy: Pull your TS3 game folder out of Documents\EA and launch the game. (If you haven't done anything in-game worth saving yet, you can delete it outright.) Don't mess with the settings at all the first time; just check to see if the map loads correctly and you can get into Create a Sim. If so, you can exit to the Main Menu, change the settings however you like, quit to desktop, reload, and start playing.
Even if you didn't do anything to your graphics settings, it's still worth pulling your game folder to see whether it makes a difference. If it doesn't, another possible cause is a typo in one of the game's .sgr files. If you edited these files to force recognition of your card, even something as simple as the wrong quotation mark could mess things up. Try putting the original .sgr files back, at least temporarily, to see if it helps.
If none of this applies, I'd like to see the first 40 or so lines of your deviceconfig, also in your TS3 game folder. You can copy and paste those lines into a post here; stop when you hit the list of game options. This file shows what TS3 makes of your hardware, as well as which graphics card it's using if you have a dual setup. Your user and machine names are listed about 25 lines down, so you can delete those if you want, but there's no other identifying information in the file.