I've been shooting crows since way back in the 60s, and I've used several different shotguns as well as chokes and guages.
My "go-to" round nowadays is a 12 guage, #7.5 shot, modified choke. I've used practically everything from #4s all the way to #9s, but 7.5 seems to be magic for me.
If the crows tend to fly high, #6 would be a good bet, but if you get them relatively close, 7.5 will do a good job since you get more shot and a denser pattern.
As well, for many years I used only a 20 guage, a Remington LT-20 with a modified choke, and then later a Browning Citori 20 guage with fixed chokes of full and modified.
There's nothing wrong with the 20 guage for crows. I've put a lot of birds on the ground with them, and still enjoy shooting 20s.
Another consideratin is recoil. If you do a lot of shooting, you may find a semi-auto more comfortable, as well as a 20 guage. Just depends on how much shooting you might do.
My advice - choose a gun that fits you well and that you feel comfortable with, one that just seems to point naturally. Then, get a modified choke and use either #6 or #7.5 shot. Do some pattern testing to see what works well with your particular gun and choke.
You may have to experiment a bit to see what is right for you. As you can see, all of us that responded have our own views. You will find what works for you.
Good luck, and we hope to see some good crow photos along with your new toy soon.