I don't give buying advice anymore since someone bought a monitor I like and he was very disappointed. So I just gave you the options you have; TV/Monitor with TV tuner or input, another second hand 1084 or a SD/FF that gives you a VGA plug (these devices are rare and expensive) if you want to keep the 1200 like it is.
Another option would be buying a busboard with video slot capabilities and then get a video card with a SD/FF. This option is very hard to find and expensive and requires a tower too.
Mind you, with an A4000 you have the same trouble. You can't just connect a VGA monitor to it; it has the same video port the 1200 has. Adding a graphics card is a lot easier though as you'd have a video slot with Zorro connector out of the box.
The easiest way for you right now to connect a 1200 to a screen would be using a composite cable from the 1200 to a TV or monitor that has composite input.