My current controller (Nelson) has a 24VAC 250mA AC Adapter. Can I use this with the AC Powered OpenSprinkler or do I need the at least 500mA which is what the adapter being sold here is? Or should I purchase the DC Powered OpenSprinkler? I have Irritrol valves with 24VAC solenoids.
250mA is pretty low. You can still give it a try. Generally 250mA is only enough to drive one solenoid valve. The controller itself also needs to draw some current, though not a lot (probably 50 to 100mA at most).