David, hate to say it but both corn and sunflowers are not great candidates for transplanting because they put down big, deep roots pretty fast. They grow so fast, most people just seed them where they will grow to maturity. There's not much to be gained by seeding them early, then risking transplant shock will kill them when you move them.
Yes, it's important not to disturb the roots too much, if you can. So planting in a container that the transplant will come out of easily is quite important. I use a dinner fork, or sometimes a fork and a large spoon, and slide them down either side of the plant pot, then "grab". Make sure the transplant is moist but not wet when you pull it out. If you can get it out with a root ball intact that will be best.
Other types of plants make a whole lot of fine roots that hold the soil around them, making them transplant much more easily.
