Are new Shimano shifters compatible with old 600 Arabesque derailleurs? Does anyone know if I can use new gear shifters, especially integrated road bike shifters, with vintage a Shimano 600 Arabesque rear derailleur? Will the pull ratio of the shifter and derailleur match? Also, should I stick to Shimano or could I use Campagnolo, SRam, etc.

Update:
I have a 9-speed modern cassette and the my frame was stretched to fit it.

Additional question: do you think the 600 will handle a 9 speed cassette?
The problem is that if you're running a Shimano 600 system, you've probably got a 5 or 6 speed drivetrain and the lowest number of speeds on a modern brifter [integrated shift+brake lever] is 7 (the Shimano Tourney brifters are 7 speed). So you'd need either downtube shifters, bar end shifters, or stem shifters (all of which likely will operate in friction mode unless you can find a Shimano compatible one which matches the number of speeds you have with the cable pull matching Shimano). I believe the cable pull is the same as modern &lt;9 speed Shimano rear derailleurs though. 

Campy and SRAM usually have different cable pull and they wont produce a brifter which is 5 or 6 speeds anyway so you're stuck with friction mode (generally, mixing manufacturers causes problems and requires pulleys to adjust for cable pull). 

Another option is (since you likely have downtube shifters) are Retroshifts, which are a way of taking your existing down tube / bar end shifters and attaching them to a brake lever. This removes the problem as well.