Hi @TempleAssassin & @mvokay - @jpkarlsen has given some helpful specs for high end and low end choices. I don't have experience with speccing specifically for The Sims 4, but I went through similar pain trying to upgrade my pc's last year (I was still running Windows Home Vista - and I'm cheap! lol)
The issue pretty much lies in getting a laptop for $500; the extreme specials you'll see out there are usually configured with low-end graphics and questionable power supplies, in order to hit the right price point. They're going to be sufficient for the typical student or adult who enjoys social networking, browsing and shopping online, etc, but anything above Facebook games is going to probably tax the system too much.
When I finally bought my gaming PC, I configured my own at CyberpowerPC. Now, I don't work for them or have any affiliation, I'm just giving you an option you may have not seen. If you post those high-low specs on their forums (don't configure on your own - ask the people on the forums) there are friendly users with a great knowledge of that site and what should be upgraded and what you can bypass. If there's a way to get a solid config at your price point, they will find it. Or, they will tell you how much higher you should probably go to get the bare minimum.
Another option is the Best Buy site, use the navigation and filters - check the minimum specs off on the side (i5, i7, Ryzen 8; 8 GBs ram, etc) and put in a maximum of $500 for the cost. When I did this, I did get some options, but all of them have the on-board graphics cards, which @jpkarlsen has said is too weak. I don't know if you will be able to find a laptop with a dedicated graphics card for under $500.
So, I guess the question for @jpkarlsen - how bad is an integrated graphics card in a laptop, for a user dedicating the computer to just The Sims 4? Can it run without major glitches with Intel UHD Graphics 620?
You can use an integrated graphics processor but at the cost of graphics quality. I recommend a dedicated card because one thing is what is required today another what may be required in the future. We have already seen an increase in minimum requirements with the recent expansions. I'm not sure we have seen the end of this. There also is the thing that you say only Sims 4 but what if there next year comes a new game you would like but can't play on a PC that is just "good enough" for Sims 4 and in a couple years we will likely see Sims 5 that are guaranteed to have higher demands. I have to keep these things in mind when recommending a PC or people might come back next year and say I gave them bad advice. Now if people decide to go under my recommendation it is entirely up to them if it turns out that they should have invested a bit more.
