I am doing web graphics for about a year on quite good PVA LCD display. 95% of people who see my websites/banners are watching them on low quality TN displays suited for gaming or laptops. Colors on those displays have much lower quality and differ a lot from those I see on my display.
My question is: Is it better to do web graphics on high quality monitors( so when I design mild yellowish background on website, normal people see it almost as white) or is there some other way how to fix this?
This isn't a UX question.
That said, I always recommend having a really nice monitor and a really crappy one. Run them side by side, and drag things in between the two to get an idea of what it will look like on a range of displays.
The problem with designing on poor-quality displays is that every poor-quality display has different kinds of problems. I expect what you're talking about is designing on a panel with relatively small gamut, but there are other issues that are equally likely to affect the quality and fidelity of colours on a display:
If you're targeting a specific device/hardware profile (as in mobile development), you really should check the output on the display itself (especially if the display uses a different kind of display altogether such as an OLED display, especially a PenTile one, since the colour reproduction can vary dramatically from a conventional LCD screen—especially saturation). There are some great tools to help you with that such as LiveView (for iOS devices) and Android Design Preview (for Android devices).
However if you're designing for general use across a very wide and uncontrolled set of devices there's no reason to suspect that designing on one terrible display will ensure better fidelity on some other bad display. It's my belief, then, that you should design on a well-calibrated, high-fideltiy display if possible and, as with any other design task, test the output in as realistic a condition as you can, on a few different displays of varying quality.
Pay special attention to the way JPEG artefacts are shown; designing on one display and choosing output settings/compression ratios in Photoshop to be unnoticeable can sometimes mean viewing on a machine with much lower gamma reveals all those terrible-looking compression artefacts plain as day.
Yes, you should use good quality monitor for designing, but it is always good idea to check the work on same settings as end user will see it.
What I find useful in monitors is "Magic Angle" option, that will show more colors.
The best monitor for designing web graphics might be on a commonly used laptop. The bulk of users will be viewing your site on a laptop so you should what they will see.
This obviously doesn't cover EVERY user but it should help you design things that will degrade nicely when people done have a top of the line external monitor.
Yes, it's better to use a decent monitor for design work than a crappy one. The reason is that crappy monitors are all different, and adapting to a particular monitor might cause your design to look worse at a different monitor. For example, when you design on a monitor that is too blue, your work will look extremely red on a monitor that is too red already.
For a design to work across a wide range of screens and devices focus on general principles (also helpful with regards to accessibility): don't rely on colour alone; use sufficient contrast; choose an adequate size, etc.
Test your design on different screens, and in different circumstances (mobile phones for example are often used in bright sunlight), and find out what works and what doesn't. Some colours are known to cause trouble (when presenting a logo in a certain colour of yellow/green a designer explicitly warned me that this colour could only be used in print or on good screens, because it would look very dirty on low quality devices).
