Do you have World Adventures, Ambitions, Late Night, and Seasons installed, and checked off in the launcher if you're on patch 1.69? (If you have a Windows/Origin install, you're on patch 1.69.) The page for the custom world lists all of those as necessary, although I don't know whether a missing pack would necessarily crash the game.
One other easy thing to check is your RAM use. When you're in Edit Town and ready to place a household, put the game into windowed mode via Options, right-click on the taskbar, and select Task Manager. Watch what TS3's memory use does as you place the household and click play. If you're seeing the number in percentages, right-click on the column header to switch to absolute numbers. Anything above 3.5 GB for the game alone could easily be the cause of the crashing.
Just to cover all the bases, it would be great to see a dxdiag on your computer. It'll list the last ten errors, including any TS3 crashes, as well as other relevant information. You can run one and then post the results at pastebin.com or another free filesharing site, and link it here.
https://help.ea.com/en-us/help/pc/how-to-gather-dxdiag-information/