Windows NT based OSes (Windows 2000 & XP onwards) have poor DOS native compatibility.
Linux + a suitable VM such as VirtualBox, DOSEmu (fast) and DOSBox (a bit slower but good compatibility).
A modern Windows version will also support the above, minus DOSEmu, hence why it wouldn't be my first choice.
Windows 98/ME will run most old DOS games and can be started in real mode, if needs be. That will probably give you the best possible compatibility wise. You can also dual boot FreeDOS which is much better than any version of MS-DOS but won't run Win9x. The main disadvantages are: insecurity, lack of support for modern hardware and the many modern Internet sites won't display on the old versions of browsers you can run on it.
You certainly don't need any special video card, although having a decent one will improve the performance of emulators which can benefit from hardware scaling. Very few DOS games supported specialist video cards. Most games were VGA 8 bits per pixel, normally 320x200, but mode X would give you up to 360x480 with a generic monitor (Quake did that, I don't know about other games but Windows 9x/ME used 320x400 on the start-up screen) , or 400x600 with a better monitor but I don't recall any games supporting the latter. Some of the later games supported VESA BIOS (Quake did) which work at higher resolutions and bits per pixel, including HD at 24 BPP. All modern cards have VESA BIOS and it's still used today for generic drivers on modern OSes.