I stick to 4:3/5:4 monitors personally =)

That is not an option. Need wider and multiple inputs monitor for XP and other systems. Please choose 1 out of 3 presented!

You mention win98/XP in thread title. but now you're citing 'and other systems'... ? ... good read about this all over here ... Windows XP systems, do you 4:3, 5:4 or 16:10?

1920x1080 - not good enough for scaling standard low resolutions of the 90s (640x480/800x600) or standard high-res 1600x1200.

2560x1440 - can do decent scaling of 640x480/1280x960, slightly worse with 800x600, because scaling factor is 2.4x*. Will have issues with full 2560x1440 (1920x1440) on old GPUs, both with performance and output (especially digital DVI).

* Ideally, you want scaling always go in 0.5x increments (somewhat less critical past 3x scale factor). Monitor scalers mostly use blurry scaling (bicubic and such) so 2 virtual pixel, for example, would still look fine, due to color mixing with aligned physical pixels. So for a quad of virtual pixels (2x2) you get 5x5 physical pixels.

I opted for a 24" Asus ProArt PA248QV monitor for my Windows XP build.

It does both 1920x1200 (16:10) and native 1600:1200 (4:3) with auto detection/switching capability.

The caveat is that it does have image processing which smooths even "pixel perfect" resolutions like 800x600. This can be tweaked via sharpness settings on the monitor to get something close to pixel-perfect, but there is unfortunately no way to turn off image processing altogether.

Not sure how it would fare under Windows ME.

Of the three, the 1920x1200 monitor is my preferred choice. These monitors can display the 1600x1200 resolution in a very clean way, with black bars on each side, and no additional scaling or processing. Most WinXP era games support 1600x1200 natively and look great when using it. Some later titles can make full use of 1920x1200 as well, since widescreen gaming on the PC started gaining traction during the second half of the 2000s.

For Win9x, the situation is a bit different, as some games from that time (e.g. StarCraft) only use a single, fixed resolution. Furthermore, even those Win9x games which do support 1600x1200 sometimes don't have enough texture detail to utilize that resolution to its full potential. This doesn't bother me personally, but some people don't like how low-res textures look when paired with overly sharp 3D polygons.

Note that you need a fairly powerful GPU to fully max out some of the more demanding titles at 1600x1200. Something like a GTX 960 for WinXP and a Radeon X800 for Win9x, assuming that you want to crank up AA and AF as well. That said, if you're ok with gaming at lower (non-native) resolutions, you can make do with a weaker graphics card. For example, 800x600 is a fitting and period-correct choice for Win9x gaming, and some 1920x1200 monitors can upscale it reasonably well.