I'm not a great fan of lactic acid and Adrenalin, that is why I favor a neck shot when possible. They go down in a pile and don't live long enough to pump the muscles full of hormones or produce much Lactic acid.
I usually hang them for at least a couple of days in the cooler, never more than three days.
Most all of my Venison ends up as Goulash or Chili. Not for any particular reason other that's what I like. It seems to get better the more it simmers and the older it is within reason. Two, three days old and the bottom of the pot is the best.
I may be full of it but, my girls and wife seem to like Lactose and adrenaline pumped Deer. I think it's a woman thing. I favor young Bucks or Doe, while the girls seem to like mature Bucks.
Old Bucks occasionally get a marinade and an over night soak.