Providing the gun is in shootable condition, CURRENT production .32/20 from Winchester, Remington, Black Hills or Ultra Max is good to go.
All of these loads feature a 100 or 115 grain lead flat nose at 700-800 fps out of a handgun.
I have shot the Winchester and Remington loads out of my 1906 production 5" .32/20 M&P and they work great, even though they are very weak. I got a nice 1" six-shot group at 15 yards with the Winchester flavor the last time I shot the gun.
In the past, there have been "High-Velocity" .32/20 loads that were unsuitable for most handguns, especially the pre-heat treat cylinders of the early M&Ps. These loads have been off of the market for years now, so if you stick to current production stuff, you will be fine.
DO NOT shoot the .32/20 rounds that your buddy found in his grandpa's old hunting box.