So far, I have been powering my steppers with a large lead acid battery, and my arduino with a 9v battery. Now I am working on a new rig, and it would be handy to run both off a 9 amp 12 volt battery. Do I need to keep the separate?
9amp battery? Do you mean 9Ah ? (It's debatable that that's large in the world of lead acid batteries(!))
That's powerful enough to hold up against the motors - try using the +12V to Vin on the Arduino and it should be OK, but 12V may make the regulator on the Arduino run rather hot. An intermediate 8V or 9V regulator with largish cap (1000uF or so) would provide more isolation of the Arduino from any supply noise the motors generate should it prove necessary (and allow the Arduino's regulator to run cooler)