@Dannirossb Dell computers are good quality, if usually somewhat overpriced. They're certainly worth buying if you can get a good deal though. HPs are not gaming computers and often don't hold up when running even moderately demanding games. I can't give you any kind of stats, but I've seen plenty of HP laptops that should be able to run Sims 3, based on the specs, and yet aren't performing up to expectations. Anecdotal evidence on other games seems to back this up.
Asus has a good reputation as well, although its products do also occasionally have issues. The reviews I saw for this model seem to say it's what you'd expect, except that the battery doesn't last as long as you'd want. But for $700, there are going to be some compromises, and I personally would prefer to work around the battery than have to deal with lower performance from the other hardware.
On the subject of TS4 specifically, the biggest improvement in performance will come from a dedicated card. Yes, an Intel 620 will run the game. It will probably run the base game on medium settings, perhaps with a few turned up to high, as you saw. But once you start adding the newer expansions to the mix especially Seasons and (from the current complaints) Island Living, performance will drop off unless you turn down the graphics. That's also true if you have a lot of the older packs—while the individual demands of each are smaller, the cumulative impact is significant.
If you really don't plan on adding much to the base game, you might be fine with a 620 or a Radeon Vega 8, but otherwise, having an MX150 will make a noticeable difference. There are probably other available models with an MX150 or 250, although I didn't see one for less than $800 when I looked, at least not with a <15" screen.
