Can anyone recommend cheap laptops that have good build quality and see lightweight?

I aim to use it for programming, but I connect to my desktop for most hefty work so it doesn't need to have solid performance. 8 GB RAM, 256 GB storage are enough for me. a lower grade CPU would still be good; a i3 that's 6 cores is enough.

What's really important to me is build quality, especially the keyboard. I also don't want it to be big. 13" would be enough, but not too picky here.

Any recommendations? And are there any communities that are better to ask this in?

Budget: I am hoping to pay $400 or less, but willing to pay $1000 or even more if it's justified or the value is worthwhile

OS: Linux. I can install it myself.