You seem kind of all over the place about what you want to hunt. Why not get your feet wet with Jack Rabbits? Wherever the agricultural areas meet the undeveloped wooded or brush areas there are going to be Jack Rabbits. Jacks are protected some places, not many but some. Jacks are actually good eating, though there isn't a lot of meat on one.
I usually hunt whatever there is the most of. It isn't a contest with other hunters, a body count or bragging rights IMO In my case it is a strong hunting instinct and most any game will do. I even enjoy Ratting with my dogs.
A lot of Dove around and I hunt Dove. The Rabbit population spikes and I hunt Rabbit. Most hunting is cyclic, a responsible hunter can smooth out the population bumps without affecting the larger ecosystem.
What I hunt the most of is Varmints, mostly Fox. You suppress the Fox/Yote population and most of the game birds and whatever rebound and the hunting gets better. In effect, as a hunter, you are in a competition with natural predators.
Crows are iffy, most places they are protected under the Migratory Bird Act. There are exceptions when they become too much of a pest. Crows are nest robbers and eat young birds. Most times hunting anything during nesting season is forbidden. If there are a lot of Crows around, it is doubtful there will be many ground nesting game birds around.
You have to commit, the more time you spend observing, the better your hunting skills are going to be. Hunting is a lot more than just shooting something. You should survey your hunting area, observe and decide what needs to be harvested. While I'm hunting varmints I watch for Deer sign, Hog sign, whatever and know where the edible game is.
Hunting is a lifestyle and to be any good at it demands a lot of time. The amount of time I spend just watching really adds up. Then there is the time practicing and improving your shooting skills. Then there is scouting and finding hunting grounds. The time I spend actually shooting anything is a very small percentage of my time and efforts.