Of the games you listed, none has requirements close to what Sims 3 needs, so you're good there. Interestingly, Best Buy had the single best deal I could find, cheaper than anything good enough on Amazon or the other sites I checked. This model is $600:
https://www.bestbuy.com/site/cyberpowerpc-gamer-master-gaming-desktop-amd-ryzen-5-series-8gb-memory-amd-radeon-rx-570-480gb-solid-state-drive-black/6343318.p?skuId=6343318
Its graphics card is actually a bit better than is strictly necessary for TS3, although if you use a lot of cc, you'll be glad for the extra power. It has a solid state drive (SSD), which will make loading times much faster than if you had a mechanical drive (HDD), both in TS3 an in general. Plus, it's upgradable later, if you want—most Cyberpower computers are meant for swapping parts. It would be easy to add RAM or a second hard drive when you decided you needed it.
You might be able to save money with a refurbished computer, but the problem is that you wouldn't know how the graphics card had been used. Given that you want to be able to play a reasonably demanding game, you do need to know that the card is in good shape, or you might end up needing to replace it soon. At the very least, be sure to get a model with some kind of store warranty or guarantee.
If you're going to look yourself, here are the specs you need:
- Processor: At least 2.4 GHz base clock speed, quad core or higher, and not U- or Y-series. If you're considering an older model, it's best to ask first, since there are too many to summarize neatly.
- Memory: At least 8 GB RAM. 16 GB is great for multitasking but isn't necessary, and it's very easy and cheap to add more later.
- Graphics card: Nvidia 1050 or higher (or 960 or higher in older models), or AMD RX 560 or higher.
- Storage: At least 512 GB total for gaming. You can put movies, music, photos, etc. on an external hard drive, or buy and install a second internal drive (also very easy); you could get a 1 TB internal HDD for $40-50. Solid state drives are very nice but not strictly necessary—your games will run fine on an HDD, if more slowly.
If you find something you're thinking of buying, feel free to link it here.