I've hunted most variety of small game and bird...I'm currently looking into bowhunting (saving $$$ for a bow), likely for larger game (deer, wild pig) and turkey.
I'm into rabbit hunting in the Mojave Desert- I'll probably be going out this Sunday. Overnight solo trips are a good way to do it- set up a camp and hunt the evening and wake up early for a dawn hunt (the most active times, like fishing). It's nice to find a high spot, take some cover, get out the binoculars, and just watch. I can pass hours doing it.
I would only ever shoot what I would eat...when rabbit hunting, if fortunate enough to shoot something that evening, I'll dress it and grill that night (the advantage of BLM land- no fire restrictions).
If I get something in the morning, I'll pack it out. I usually have an ice chest waiting in the car. Like fish, mammals should be cleaned/cooled immediately if they're getting eaten.
I really don't see much difference between hunting and fishing- I do both...same idea, different tools/prey.