If you want to use the A2000 with a VGA monitor, but can't or won't by a Zorro II based video card (they can be prohibitively expensive). Then might I suggest you look into getting a used flicker-fixer and/or scan-doubler (de-interlacer). A flicker-fixer/scan-doubler (FF/SC from here on out) will take the RGB signal, de-interlace it and bump the frequency up to 60Hz (most mult-scan VGA displays still sync this low - NPI).
I used one on my A2000 for quite a while before I bought a video card (the rather disapointing GVP Spectrum 28/24). While I'd never want to go back to just a FF/SC permanently. A FF/SC will allow your A2000 to drive a VGA display 'acceptably'.
You can find out a bit more about many such devices
here (along with a lot of other Amiga hardware). Keep in mind that not all the devices on that page are FF/SC's.