Sims 3 keeps crashing (Solved)

@Pluviophist I don't know anything about GeForce Shadowplay, but it's entirely possible that it's causing all of your issues.  Definitely try disabling it first, before moving on to the other interventions.

If that doesn't help, I would like to see that dxdiag, as would anyone else who comes along.  You can attach the file to a post here using the Browse button.  The info in there will help eliminate certain causes of your issues; otherwise, it's really kind of a guessing game until something works.

In the meantime, I hope you did a clean uninstall before reinstalling the base game.  If not, it's a good idea to uninstall and clean the registry, either manually or with a tool like Piriform's CCleaner, just to keep the troubleshooting simple.

https://help.ea.com/en-us/help/the-sims/the-sims-3/manually-uninstalling-the-sims-3/

It's also a good idea to test the game in a well-made world like Sunset Valley, Riverview, or Twinbrook.  Bridgeport does have a few issues with elevators and NPC rooms in the apartment buildings, although those alone shouldn't be causing the UI error.