@Lyrie18 Don't worry about the delay; people come around when they have time, and someone will be here to help.
If the Lenovo you linked is in your price range, you can certainly get what you want. There aren't nearly as many options for gaming laptops with at least 1 TB storage, but there are enough. For some reason, all the cheapest good options I saw have 15" screens, not 17", but it sounds like that would be fine too. (Let me know if it's not, and I'll look again.)
So there's one other decision for you to make, and that's whether you want an Nvidia 1650 or a 1660 ti or higher—a couple of options with a 2060 are cheaper than their counterparts with a 1660 ti. Even the 1660 ti is overkill for Sims 4. However, the 1650 is right on the border of what we think will be necessary to run all current and future TS4 packs together on ultra settings. So if you'd like to futureproof, you might wnt to spend the extra for an upgrade. Additionally, if you would like to run the game ith higher fps than 60, the 1660 ti or 2060 would be a better choice than the 1650.
Most laptops with a 1650 wouldn't have 1 TB of storage unless they only had a mechanical drive, or else a very small solid state drive paired with a 1 TB HDD. If you want more SSD space, the cheapest option is to go custom. This Cyberpower has a 500 GB SSD standard, but upgrading to the 1 TB WD Blue NVMe SSD would cost $13 extra ($968 total). It has 16 GB RAM and the same powerful processor as the Lenovo does.
https://www.cyberpowerpc.com/system/Tracer-III-15V-VR-200
Other than that, I didn't see anything with a 1650 that's cheaper than the first options with a 1660 ti. This Asus, for $972, has a much weaker processor than the Lenovo or the Cyberpower, but it would still be more than good enough for Sims 4. You might notice a difference in other games though, or if you wanted to do video editing.
https://www.amazon.com/ASUS-IPS-Type-R7-3750H-GeForce-TUF505DU-EB74/dp/B07QQB6DC1/
This MSI has the same specs as the Lenovo but is currently (looks like only untl the end of today) on sale for $1,169, plus an additional $100 rebate. It's still cheaper than the Lenovo even without the sale though. I will say that the Lenovo gets slightly better reviews—I looked up these same two models for someone else a few weeks ago. The laptops are still very close in terms of performance though.
https://www.newegg.com/aluminum-black-msi-ge-series-ge65-raider-431-gaming-entertainment/p/N82E16834155330?Item=N82E16834155330
You could get the same Lenovo, except with a 15" screen and the faster Nvidia 2060, for $1,200 on a different site:
https://www.bhphotovideo.com/c/product/1462365-REG/lenovo_81sx000fus_15_6_legion_y540_gaming.html
Cyberpower also offers this model with a 2060 and a free upgrade to a 1 TB WD Blue SSD. It's $1,099, cheaper than any of the options with a 1660 ti once the upgrades you'd want are applied, and has the same strong processor and 16 GB RAM.
https://www.cyberpowerpc.com/system/Tracer-III-15Z-Slim-VR-300
If you have any questions about these options, please feel free to ask. And if you're wondering about the recommended specs for the other games you'd like to play, you can list those games, and I'll see what kind of hardware you'd want to run ultra settings.