The .410 will work if your' re a better than average shotgunner. 12ga can be a bit " big" for dove. I prefer 20ga for birds in general, but the 12 has such a big pattern that it is usually more effective for a larger number of shooters. Just make sure you' re using the right shot size, #7 1/2 or #8 should be fine. With a 12ga you could even use #6, but once you get much bigger, pattern density becomes an issue to consider.
Then there the economics.....out here, 12 & 20 are the cheapest shells unless you reload. And when it comes to dove hunting, you will go through a lot of shells.
Some shooters can go through a whole box w/ nuthin to show for it but 25 empty hulls, other guys get doubles almost every day they shoot.
Have fun, and don' t forget your ear plugs.