@Barbella_36 Your price range is definitely fine, although there's usually a significant dropoff in quality at or just below the $600 mark. That's the difference between a laptop having a dedicated graphics card and not, and a dedicated card will run Sims 4 (and almost any game) much better than an integrated one. If you do want options below $600, I can find some, but they're not going to be as good as the models listed below.
This one is as low as I'd go, at $600. It has a decent graphics card, one that would likely run Sims 4 and all packs on ultra settings, although maybe without much room to spare. Its processor is fine too.
https://www.bestbuy.com/site/asus-fx505dd-15-6-gaming-laptop-amd-ryzen-5-8gb-memory-nvidia-geforce-gtx-1050-256gb-solid-state-drive-black/6338249.p?skuId=6338249
At $700, you could get a much stronger graphics card, one that can certainly handle ultra settings without any trouble now. In fact, it might be able to handle all packs, now and in the future, on ultra, depending on how the game develops; the Nvidia 1060 3 GB is right on the edge of what is recommended to futureproof for those packs. If you don't intend to get most or all expansion packs though, it should always be fine. (Game and stuff packs don't increase the demands nearly as much.) This also has a slightly better processor than the previous one.
https://www.newegg.com/p/N82E16834235081?Item=N82E16834235081
The one drawback these two laptops have is their small hard drive. While 256 GB is enough room for Windows and Sims 4, you wouldn't have enough space for a whole lot more. Browsers and text documents would be fine, but a music or movie collection would not be. But you could use an external hard drive for those, or buy a second internal hard drive for the computer. (This is easy with these laptops.) You could find a 1 TB HDD on Amazon for maybe $45, or pay a bit more and get one at a computer shop that would also install it for you.
If you don't want to get a second hard drive, internal or external, here are some other options. This one, at $670, has a weaker graphics card than the one above, and the same processor. Its hard drive is large, 1 TB, but it's a slow mechanical drive. While this wouldn't make much difference to TS4, almost everything else would run slower, including Windows. HP also doesn't have a reputation for making great gaming laptops.
https://www.amazon.com/HP-15-6-inch-Anti-Glare-WLED-Backlit-15-cx0056wm/dp/B07KQXHP4M
This is the same idea, except with a much stronger processor:
https://www.newegg.com/obsidian-black-acer-aspire-7-a715-72g-73y5-gaming-entertainment/p/N82E16834316524?Item=N82E16834316524
You could also get a laptop with a combination of a small, fast solid state drive, plus a large mechanical drive for extra storage already added in. These two have that same 128 GB SSD/1 TB HDD combination. The first has a slightly better processor and a graphics card that falls between the 1050 ti and the 1060 3 GB. The second has a 1060 6 GB, the strongest card of all of these, and one that should always run all Sims 4 packs on ultra settings. They're $780 and $800, respectively.
https://www.bestbuy.com/site/acer-nitro-5-15-6-gaming-laptop-intel-core-i5-8gb-memory-nvidia-geforce-gtx-1650-1tb-hard-drive-128gb-ssd-obs-black/6344387.p?skuId=6344387
https://www.amazon.com/Dell-Gaming-Laptop-G5587-5859BLK-PUS-Anti-Glare/dp/B07CD3MRZD
I know these are a lot of options, but I wasn't sure how large a hard drive you wanted, or if you'd be willing to add a second drive after the fact. If you have any questions about these, please feel free to ask.