Hello,
If you don't have a flickerfixer-scandoubler in your A2000, you will only be able to display PAL or NTSC interlaced screens with a generous overscan, and get a sufficient resolution for web browsing (around 700 x 550 pixels). But you will only display 16 colors which will make pictures and web pages a little ugly. A flickerfixer scandoubler will be easy to add to your setup and will allow to display flicker-free screens onto a modern VGA screen, which will improve a lot. But you will stick with the only 16 colors.
The A1200 is theorically able to display 256-color screens but graphics will be very slow and experience seems to show that 64 colors is a maximum for a best speed-color compromise. The A1200 still has interesting Dblpal/Dblntcs modes which can be flickerfree and displayable on a compliant VGA monitor.
A graphic card such as the Cybervision 64/3D will bring dramatic display improvement with rapid high resolution - high color graphics, even on a Zorro-II based machine such as the A2000...
