For lightweight, go with X2.0 series. I've used X200s (OpenBSD, Linux), X220 & X250 (Linux), and can recommend all of these. X230 is supposedly also decent, and can be modded with the old X220 keyboard. Avoid X240, it has a very shitty touchpad.
For sturdy, go with any older model, up to & including X220 should be fine. Newer models usually have SSDs out of the box. It's trivial to swap one in with older models, eg. with X200s it's removing a single screw to access the bay.
