@Kariva Don't get the 1030; it wouldn't run the game on ultra graphics settings, at least not very well if you have most or all expansions installed. The others would run all current content on ultra. The 1650 may be cutting it a bit close by the time the game is out of development (we don't know how demanding future packs will be), but the desktop version of the card will likely still be able to handle ultra settings.
What power supply do you have in your computer: manufacturer, wattage, and rating? If you're not sure, and the manual doesn't specify, you can just physically look at the PSU; it's where you plug in the power cord. A lower-end power supply might not be able to support some of those cards listed. On the other hand, if it's strong enough, you might be able to save a bit of money by getting an older AMD card instead, although those do draw more power than the equivalent Nvidia cards.
If you'd like suggestions for a specific version of any of these cards, let me know what country you're in, and I'll have a look around.
P.S. It's not the fact that your integrated graphics chips isn't recognized that makes the game run poorly, it's that the card is quite slow for Sims 4. Getting it recognized would be quite simple and maybe only take a couple minutes, but it would only help marginally, if at all.