I don't like raw fish so I don't go to Sushi restaurants. I don't care if it's cool, or my buddies do it. It's not "for me".
Because of that I can't see why you would say that you want to get into hunting when you obviously have an issue with killing small bugs, much less a higher order animal.
I could tell you that fully 1/3 of deer don't survive the winter due to malnutrition, the elements, predators etc. Another percentage will get "run over" causing many dollars worth of damage to vehicles. They will all still be dead/killed with no intervention on your part.
But if the thought of being "responsible" for shooting Bambi is just too much for you, then perhaps find a different sport/hobby.
You could always get yourself a bow and join a 3D club if you "want the feeling" of stalking, getting an animal in your sights and then doing no harm other than to a foam insert in the target that "looks like a deer, bear, hog etc".
Hunting isn't for everyone. In fact I don't know anyone that decided to take it up "later". If they didn't go with Dad/Grand Dad, even if they quit for a while to work or raise a family etc (which I see as "didn't go hunting" as opposed to "stopped hunting"), then they don't generally decide one day in their 20's or 30's that maybe hunting is something they want to try. Not saying it never happens but if it wasn't ingrained it's pretty steep curve on many levels.
As suggested, if you really want to give it a go, maybe ducks/geese (since you say you hate birds) - there are some "waterfowl hunters" that hunt nothing else and count down the days to the duck opener