Are there better laptop screen resolutions for gaming on a PC?
If your laptop is primarily for gaming, I would get the highest resolution screen you can afford with at least a resolution of 1920x1080, with the performance that can back up 1920x1080 at native. If your budget doesn't permit that price/screen/performance matrix consider a more affordable laptop with a 1366x768 native screen.
If your laptop is for more than just gaming, I would get at least a 1920x1080 screen. If the laptop can't handle the games at native then run your games at lower resolution. This has the effect of a bit of blur in the upscale to native, but you also don't sacrifice your productivity with non-gaming tasks.
I would suggest reviewing all of the different opinions that have collected on this question to get well rounded advice.
I think 1440x900 is a good size for a monitor. It provides a high quality resolution whilst not being too large that the graphics card, which is likely to be less powerful that a desktop version, won't get stressed out.
My concern with high resolution screens (~1920x1080+) is that the graphics cards will not being able to provide enough grunt and you will have to degrade the overall graphics quality to get a stable framerate.
Screen resolution should be taken into account only after you take into account the size (in inches or centimeters) of the screen when it comes to laptops.
With higher resolutions comes more pixels crammed onto the screen. If you have a 15.6" laptop, 1920x1080 may look great to some people, but for others it may not. This is because with such a high resolution, at native settings (max resolution), everything in the game may be very small (because so much is fit onto the screen), too small for some people.
For this reason, you should have a look at laptops in person before you buy them if you aren't sure. You may find that you are happy with 1366x768 on a laptop, and you find 1920x1080 makes everything on the screen too small!
The problem with purchasing a high resolution screen, and later deciding that you want to run it at a lower resolution, is that it will typically look much worse if you decide to run at a resolution lower than the native (maximum) resolution. You want to make sure that the laptop you buy has a resolution that you will always be running if you are visually particular. If you aren't too picky, then running a lower resolution might not bother you too much.
Running a game at 1366x768 on a screen that is natively 1366x768 will look much better than running it on a screen that is natively 1920x1080.
When it comes to gaming laptops, purchasing a larger one (dimensions wise) is usually ergonomically better unless portability is a major factor. The larger screen will give you a much better gaming experience, and the extra space on the keyboard can be very welcome to a gamer. High end laptops typically come in larger models anyway.
All that said, I would personally recommend as high of a resolution as you can get, so long as the laptop has the Graphics Processor to support running games at the maximum resolution. But it all comes down to personal opinion. Definitely go for a high resolution screen if you are getting a laptop that is 17" or larger, though.