A later-model 1084S is probably your best bet for picture quality and resolution compatibility. There's only one RGB input, though, so you'll need to swap the cable between your 500 and 600 by hand (make sure everything's turned off first). The C64 can plug in directly.
If you're going the LCD route and if you're not in North America, something with SCART and S-Video inputs gives you the best chance for success. The C64's Y/C video output is S-Video in a different connector shape. You can probably find a cheap adapter or build one yourself. For the Amiga, a simple Amiga-to-SCART video cable will do. Make sure the screen supports a 50Hz refresh rate, otherwise PAL video won't work. I'd guess that if the monitor supports SCART, though, it'll support 50Hz.
