Lots of people from NYC suburbs and Long Island head up into the nearest forest every hunting season and accidentally shoot each other, maim animals and don't have the stamina to chase them to complete the kill, etc.
If you're concerned about food shortages, it would be much easier to raise a few backyard chickens or rabbits if you have the small amount of space required for it. Much less likelihood of a gun accident that way too.
If you're set on going out in the woods for a "mental cleanse" and to kill an animal, you could do worse than starting with a read of Jackson Landers' excellent Beginners Guide to Hunting Deer for Food (https://www.amazon.com/Beginners-Guide-Hunting-Deer-Storey/d...).