It somewhat depends on the brand you select, but 1" would likely be safe, 3/4" would be tight, and neither one would likely work if you want to install an escutcheon on the wall to hide the hole around the pipe coming out of the wall. To be safe, the pipe must be bottomed out to the stop inside of the valve, and not all of them are the same depth. Then, you have different thicknesses of compression nuts and need some additional depth to have room to get it on before tightening it. The installation instructions don't seem to mention it except for push-on fittings, and those often want about 1-1/8", but again, not all are the same (you tend to need more length for a push-0n than a compression to stabilize the pipe and fitting).
Note, if the old ones are soldered on, you can unsolder them, and clean up the pipe end, then, should have enough depth for a compression one (or reinstall a new solder one). If they're threaded...just buy new threaded ones.