I didn't see your comment before I went to bed, so sorry for the late reply. $800 U.S. is absolutely doable; in fact, you could go under and still get a good enough computer.
This is the lowest I'd go—its graphics card, an AMD RX 580 4 GB, is the minimum you'd need to ensure you can always run all packs on ultra settings. It has a very good processor and a 500 GB solid state drive; SSDs are much faster than HDDs, which won't make a difference for TS4 but will make any TS3 loading (entering CAS or Build/Buy, loading saves, traveling, using Edit Town) much faster, and Windows will run a lot more quickly as well. It's $635.
https://www.amazon.com/SkyTech-Archangel-Gaming-Computer-Desktop/dp/B07JYF2394
These two have stronger graphics cards but otherwise the same hardware as the one above. The Nvidia 1660 is a bit more power than you need, but you might want it if you really like using high poly custom content (the detailed, harder to render items) in TS4. The 1660 ti is even a bit stronger than that, definitely more than necessary. The models are $750 and $800, respectively.
https://www.amazon.com/SkyTech-Blaze-Gaming-Computer-Desktop/dp/B07RHBLV7F
https://www.amazon.com/SkyTech-Blaze-Gaming-Computer-Desktop/dp/B07RL4K6CN
All of these models only have 8 GB RAM, which is enough to play either game but maybe not for much multitasking. (For example, music or a browser window would be fine; editing your screenshots while playing might be pushing it.) But it's easy enough to add another identical RAM stick if and when you need it. You should be able to find one for $50-60 on Amazon, once you know the model number in the computer, and installing it is simple.
The reason these computers are so cheap is that their other parts (power supply, motherboard, CPU cooler) are the minimum necessary for the rest of the hardware. That's fine if you just want the computer to run as is and aren't interested in upgrades. If you do want to upgrade later, or at least want the option, I can find some models that would make that easier. Of course, they'll be a bit more expensive.
Anyway, these models will all handle TS3 and TS4 just fine. If you have any questions or want more details, feel free to ask.