I think it can depend on the monitor. I have Deltaco VGA to HDMI I could try on my ultra wide benq if it would be of any help.

I was a little disappointed in the converter when I first tried it though because it didn't seem to show bios' resolution mode what ever that is and ATM I had no other screen...

The GPU in a machine that old likely can't push a low resolution that the monitor will display, so you are better off not using that monitor. You can still get 4:3 monitors, with LED from manufacturers who sell business PCs and you can find the older 4:3 LCDs at thrift stores or online resellers.

I made a test with my Deltaco converter and you can send 640x480 resolution in 60hz and also tried 800x600. In the monitor I chose keep aspect ratio and it looked fine. Also in my ATI rage pro (laptop version) I could manually change the aspect ratio of the monitor.

Alas it does not work in DOS probably because the resolution is not supported which kind of makes this converter useless for me.

But as I first said, it depends on what hardware you have.

Thank you both for your answers.
Well yes, it depends on the HW as well, however this is still under discussion, I might get an "entry level" VGA at first and then move on to an ATI Rage or Riva TNT2 Ultra, those would be my targets for now.

On the other hand, yes, you can still find LCD monitor for a bargain, problem is space, eventually 😀