Your best bet to test it out is an old A520 composite adaptor from an Amiga 500.
Doesn't the 4000 have a built in composite port? :-? The 1200 does, and some older Amigas have a monochrome one.
For multiscan monitors, I recommend the CEI 1962, AKA Electrohome 1440, AKA Amiga M1468 (or something like that). Decent picture quality, and it's true multisync, from 15KHz to 31KHz+, so even Super72 will work (useful for big screens without a GFX card.
In theory, OS3.9.2 can promote the Early Startup Menu up to 31KHz, but I haven't had any success with that on my 1200. If you can get that to work, you can even boot the machine into DblNTSC or DblPAL for old games. If you can get all this working, and use Mutiscan or similar for your Workbench screenmode, you might be able to surive with a standard VGA monitor. This might be a good temporary solution.
Like Jeff says, though, the PicassoIV is probably the best choice compatibility-wise, and in terms of ease-of-use.
