You also might want to watch this video by the 8-Bit Guy.
If you intend to use the laptop as a desktop replacement and connect an external monitor, then you shouldn't have to worry about the built-in display.
I have laptops with these awful passive matrix displays and they're just terrible for any game with moving graphics. Even stuff like Cosmo's Cosmic Adventure (which runs at 9 fps) is pretty much unplayable on these displays. If you thought the early TFTs were blurry, these are beyond blurry. And the image quality seems to get worse over time, just look at this:
See those vertical bars? This seems to be a common problem with old passive matrix displays.
If you're going to buy a laptop with a passive matrix display, try it before you buy it. Let it display something with high contrast for a while and see if the image gets worse after a couple of minutes. Run a game on it and see if you can/want to live with the blur.
If you're able to test it, you should also prepare a floppy/CD with a few programs to test for compatibility. For DOS games, that should include:
- something to test if PC Speaker, AdLib sound/music and SoundBlaster sound effects work correctly (Wolf 3D or Duke Nukem 2)
- something to test if EGA/VGA panning and split-screen features work correctly (Crystal Caves, for example)
- VESA SVGA tests (Quake, Duke 3D)
Don't take anything for granted. I have a late 90's laptop that plays absolutely no sound in DOS mode, not even PC Speaker beeps (Sony Vaio PCG-F305). Both my Sony Vaio's (PCG-F305 and PCG-9451) can't do panning (which is used for smooth sideways scrolling graphics) in combination with the display's hardware scaling, but connecting an external monitor and using only the external monitor for display avoids that (the BIOS doesn't have a setting to disable the scaling). And I also have a laptop that doesn't support the split-screen feature (Fujitsu Lifebook C325), which means games like Crystal Caves, Secret Agent, Hovertank, Catacomb 3D and Vinyl Goddess of Phobos are missing the status display at the bottom of the screen and are unplayable (connecting an external monitor doesn't fix this). Some earlier laptops also come with very little video memory, so you can't use any hi-res SVGA graphics modes on them (chances are they're too slow for SVGA graphics anyway).
So yeah... using a retro laptop for retro gaming might be more convenient than using a desktop/tower PC, but actually getting all your games to run can be a nightmare due to incompatibilities. I don't think it's possible to find a laptop that will be able to run DOS games and 3D-accelerated games like Q3 and UT. Any PC fast enough for Q3 will probably be too fast for some early 90's DOS games, which means you'll see many "divide by 0" or "runtime error 200" messages.