@flyingtrashcan03 There isn't a lot in that price range; even used entry-level gaming computers tend to be a bit pricier. I did find exactly one good option on Amazon, from a third-party seller but with the "Fulfilled by Amazon" tag. This computer is $350 and has a good processor, slightly better than the strongest one among the options you listed; and a graphics card that's significantly faster than any of the three you saw.
https://www.amazon.com/HP-750-411-Desktop-i5-6400-Windows/dp/B01LZWMNZM
If you're willing to shop on Ebay, however, there are too many good options to list. Here's a sampling, with the best one last:
https://www.ebay.com/itm/Dell-XPS8930-7401BLK-Intel-Core-i7-16GB-RAM-2TB-HDD-GTX-1050-Ti-Windows-10/303353460205?hash=item46a14675ed:g:-EkAAOSwlEBcQVqc
https://www.ebay.com/itm/CUSTOM-Gaming-PC-Ryzen-3-1200-Nvidia-GTX-1060-3TB-8GB-RAM-RGB/113948815522?hash=item1a87e0f0a2:g:ctsAAOSw~mBdrbfQ
https://www.ebay.com/itm/Mini-Intel-i9-9900-Gaming-Desktop-PC-Eight-Core-Computer-SSD-GeForce-GTX-1060/274086798694?hash=item3fd0d8a566:g:g0oAAOSwEzNdAwrl
(Quite frankly, the third one should go for a lot more money than the current bid; its processor alone is worth $500 when new.) All of these, if they are what their descriptions say, would run Sims 3 and all current Sims 4 packs on ultra graphics settings. But of course the flip side is that you're taking a risk by buying on Ebay.
If you'd like to comparison-shop a bit more, here's a rank of graphics cards to look for, in order of increasing strength:
AMD RX 560 < Nvidia 1050 < Nvidia 1050 ti < AMD 570 or 480; Nvidia 1060 3 GB < AMD 580; Nvidia 1060 6 GB
For processors, any Intel at least 6th generation i5 or higher, or 8th gen; or anything in the AMD Ryzen line, would be fine for both games, as long as it doesn't have a U on the end of its name. It's a bit more complicated than that—obviously, newer CPUs being stronger than older ones, but an i7 or Ryzen 7 is better than an i5 or Ryzen 5. At any rate, if you stay in this category, you'll be okay.
If you do find something you're considering and want an opinion, feel free to link it here. That goes for Ebay as well as any other site. But it's a lot easier to look at a link than just the listed specs.