@infinitespectral It's not too difficult to find a laptop for Sims 4 for significantly less than $800, but for Sims 3, things are a bit more complicated. Until the most recent generation, the game didn't run well on integrated graphics, although the outcome varied widely from one player to the next. With the 11th-gen Intel processors, I've seen what looks like much better results, and one person whose information I trust was able to play on high (but not ultra) graphics settings with all packs installed. However, I'm still not sure that this is always true even on that particular graphics chip, so I don't want to tell you it will be fine for sure.
On the other hand, if you're not going to install Pets or Seasons, you shouldn't have any trouble running Sims 3 on the current fastest integrated graphics available. In that case, or if you don't mind having to potentially turn down some graphics or make other adjustments, a laptop like this one ($650) would do well:
https://www.walmart.com/ip/HP-15-6-FHD-Intel-Core-i7-1165G7-8GB-RAM-512GB-SSD-Silver-Windows-10-15-dy2172wm/649015725
It should run Sims 4 on high settings without any trouble—that game sizes down well—and it's the same chip as the person whose reporting I trust has. It also has 512 GB storage, which you'll definitely want if you're planning to install both games and also have room left over for school. Other laptops with the same Intel i7-1165G7 processor should perform the same, give or take a few percentage points; let me know if you'd like to see more options similar to the one above.
You could instead get a true gaming laptop, one capable of running both games on ultra graphics settings with some room to spare. I'm seeing a few options for $700 or less with only 256 GB storage, which would likely be a tight fit once you installed your custom content and built up a few saves. Unfortunately, the options with 500 GB storage are mostly $800 or significantly higher.
https://www.amazon.com/Acer-AN515-55-53E5-i5-10300H-GeForce-Keyboard/dp/B092YHJGMN
https://www.walmart.com/ip/797151449
The graphics card in these two is more than fast enough for both games; in fact the older Nvidia GTX 1650 would also be more than fast enough, but I'm not seeing much stock in new laptops with that card and enough storage. As far as used options go, there are plenty, but I'm hesitant to recommend one from a third-party seller on Amazon with ratings hovering in the low 80s.
This laptop is $750 and has the same graphics cards as the one above. Its build quality isn't quite the same, although it should still be more than fine as long as you don't let it overheat (i.e. don't play on top of blankets or while the laptop is inside a case).
https://www.walmart.com/ip/744908020
If you don't need the laptop right away, you could upgrade this one to have more storage. It has a 1650 and a $600 base price; going to a 512 GB costs $70 extra.
https://www.hp.com/us-en/shop/pdp/hp-pavilion-gaming-laptop-15z-ec200-2r1x7av-1
If these aren't quite what you're looking for, let me know what other details matter to you, and I'll do another search. And if you have questions in general, please feel free to ask.