Which of these laptops would work, please?

@hurley8604  The second one is definitely the best of the three in terms of internal hardware; its graphics chip is at least 50% faster for gaming than the one in the first laptop, and maybe 40% faster than the chip in the third laptop.  While Sims 4 should run fine on any of these, the gap in speed is the difference between medium and high settings.

Sims 3 is another story entirely.  I can't actually tell you for sure how the game should run because I haven't heard reports from anyone with this particular processor and graphics chip.  However, I do know that the last-gen version of the chip, what you see in the third laptop, struggles to a significant extent with the Seasons expansion, specifically rendering inclement weather.  A number of people with that kind of hardware have to disable Seasons entirely, and Pets as well, which is even more demanding; others avoid long-haired pets and disable inclement weather and seem to do okay.

There are probably some players who run all Sims 3 packs on laptops like this, on lower settings, without much crashing.  The differences are partly due to the manufacturer and model of the laptop—the support software can be quite different, as can be the cooling—and probably partly due to chance, as in, not all laptops are exactly identical due to slight variations in the manufacturing process.  The point is, you can't count on any of these laptops to run all Sims 3 packs well, although you might end up having a good experience.  And if you don't want to play with Pets and Seasons, your chances of success rise considerably.

If you'd like to see other options, let me know what features and details matter to you, and I'll have a look around.  Do you need a touchscreen?  Sims 4 doesn't work particularly well with one; I'm not sure how Sims 3 handles it.  I'm guessing you want a lightweight laptop, but please list anything else important.

@puzzlezaddict Thanks for all the information! Pets is one of my favorite expansions, and I love the long haired animals, so I definitely want something that can handle that.

The second one is in stock near me, so I might go try the keyboard out tonight. I'm so used to having the keypad to the right, that when I use one without, I'm always a key off when typing. But it's possible that it's set up in a way that it won't be an issue. 

I would like a lightweight computer. My current one is a beast (and also about 6 years old).

Touch screen is not necessary.

A medium-large screen so I can actually see what I'm doing. I think my work laptop is a 14 inch, and that's good for me. (It's an HP Spectre, but no idea what model)

Two USB ports so I can plug in a mouse and have the option for something else. 

CD drive (but I feel like these don't exist anymore). All my Sims 3 are hard copies. But I think since they are registered I can redownload them?

@hurley8604  You can certainly download your Sims 3 content from Origin if it's showing in your game library.  You could also install via disc using an external disc drive.  Which is the better option is a matter of personal preference: many people would prefer to avoid Origin, and many would rather not deal with discs.  You don't have to decide now though, especially since laptops generally don't have internal disc drives anymore, and the lightweight ones almost never do.

Let me know what you think of the keyboard, whether you would definitely prefer a number pad or think you can get used to one without.  I'll look for other options later today.  Please also let me know whether you'd be okay waiting a few weeks for a custom-built laptop from HP—there might be an available upgrade to one of their standard configurations, but the laptop wouldn't ship right away.

@puzzlezaddict the keyboard worked really well. It was spaced well and when I tested it I wasn't off on any letters. I had trouble with the delete key, but eh, of all the keys, I can work with that. 

I do not mind at all waiting for a computer. Thank you for your help!

@puzzlezaddictThank you for everything! I went ahead and ordered the Asus computer. Again, thank you for all the research and help. Can't wait until it arrives (have to wait a few days) and I can start playing!