It's hard to predict the quality of whites because it depends on the ageing of fluorescent lamp. But all laptops with TFT screens ("active matrix") are superior to everything else. STN screens are a joke and are totally useless for games or multimedia. But they could be even $1000 cheaper (originally) than TFT screens.
Look for laptops which are "active matrix" models, they can be also identified by having only the brightness slider and no contrast regulation. I have experience with these:
Texas Instruments Travelmate 4000M (active matrix color version): 640x480, 10.4 or 9.4 inch, 486DX75/100, Sound blaster compatible, SCSI port, CD-rom docking station
Siemens Nixdorf PCD-4ND, PCD5ND: 10.2 inch TFT screen version, 640x480, 486 or P1, sound blaster compatible
Toshiba T3200SXC (1990): world's first? laptop with active color TFT screen. 386SX. Unfortunately probably all of these screens failed after years and display only pale white image. But it worked just fine with a replacement industrial screen after rewiring connectors.