In order to answer your questions about monitors, I'll have to ask a question regarding where you live.
Do you live in Europe or some other country where the PAL or SECAM signals are standard?
If so you can get an LCD TV with a built-in scan doubler. The color might not be as good as a 1084S used to be but it has deinterlaced graphics that the 1084S never had.
Also, the systems that AmiKit sells may be European PAL systems so if you try to hook it up to the composite signal of an NTSC monitor/TV you WON'T get a color signal due to the fact that PAL and NTSC have incompatible chromanence signals.
If you live in a country that uses the NTSC standard, things aren't so rosy. NTSC systems are more rare than PAL and you'll have to buy an external or internal scan doubler for your A1200 because LCD TVs sold here don't support PAL/SECAM scan rates and, therefore, won't be able to play most of the games written for a PAL Amiga.
In short, if you're in a PAL or SECAM standard country you've got it made as far as monitors are concerned. If you live in the U.S.A., Japan, or Canada you're in trouble.