I wouldn't necessarily recommend something like my old Asus, then, which was an all purpose laptop. I kept it for a long time, but the internal disk drive was faulty when I got it. I had to send it off three times for repairs before they would finally replace it (wiping everything each time). From then on it was fine, but over its lifespan it picked up some... Odd quirks. Like how it didn't go into sleep mode properly. Good luck turning it back on, especially if you didn't want to forcefully shut it down because you would lose something. It then stopped shutting down properly. It was hard to get it to turn off properly.
And this is just my trouble with one store bought laptop (which ran 4 and many other games just fine, I might add). I've known others to have a lot of trouble with store bought standards as well, and if I had to guess you have in these last two cases. (You bought those models as is rather than reconfiguring anything, right?)
Since it is a confidence thing, I'd want a really good warranty/the seller to test my laptop before sending it to me. I'll bring up Xotic PC again just because it is what I and my brother used and we both had a good experience. They have standard configurations starting around $800 from what I remember, so nothing extra like mine required. I understand why it would be undesirable, though, so I am also going to recommend Trustpilot, a review website, and to pick a seller with reviews that makes you feel confident.