For several years, I've started seeds in eggshells, and it works great! I carefully crack off the tops of the shells, rinse them out, and punch holes in the bottoms with a metal skewer. Set the end of the egg on a sponge when you punch the hole; also, the hole punching should be done when you first empty the shell (once it dries, it becomes more fragile and shatters easily). Fill with dirt and plant. For ease of watering, I set the shells into styrofoam egg cartons that have 1/2" holes cut into the bottoms of the wells (these are reusable for many seasons), and set those into plastic trays. (If you get a rectangular sheet cake from a grocery store, the lid from the plastic container conveniently holds 2 egg cartons.) Water from the bottom. When ready to pot up or transplant to the garden, crack the shell all over but leave it intact and plant the whole thing. The plant roots grow through the cracks. No transplant shock!

I use 1/2 gallon orange juice paper cartons. The nice ladies at church save them for me. They like to help and recycle with things they usually throw away. (they also save shopping bags for me to bag my sales in!)Throw away the plastic lid, cut them in half lengthwise to make two long trays from each carton. 5 halved cartons will fit in a no holes flat, covered with a clear germination dome. So you can do 5 different kinds of seeds in there, and take them out as each one germinates. I dip all the cartons and flats and domes in 1 T Physan 20 to one gallon of water. Then fill with a good seedstarter mix that's sterile-like my favorite Promix PGX with biofungicide. If using promix with biofungicide, fill containers with soil and water in the kitchen sink with warm water until moist. Don't use Physan or it'll also kill the biofungicide built in. If using other mix, fill with soil and water in using 1t Physan 20 to 1 gallon warm water. Then plant seeds. As a tip, don't put seeds in there too thickly or no matter how much light you put them in,they will be spindly when they are overcrowded. 50-75 tomato seeds, banana seeds, or other large plants is max. You can sometimes put up to a seed packet of small seeds like snapdragons that grow slowly as seedlings. If you're doing tropicals that take a long time to germinate, presoak them for 15-20 minutes in 1 t Physan to 1 gal water to sterilize the outside of the seeds to give them a better chance not to mold before they come up. Then cover with the dipped cover and here's the cool part, put them on your FREE heat mat! My FREE heat mat is my forced air central furnace with floor ducts. You take a empty web flat, the ones that look like mesh on the bottom, turn it over and sit it on top of the heat vent. Then you sit your germination dome covered flat on top of it. The heat will heat your flat and also your room because it can go through the mesh flat. Check your seeds every day, and get them in bright light asap and uncovered asap. I put them out into my greenhouse. You can use bright fluorscent lights etc as an alternative. When you're growing on your plants, you can carefully take a sharp knife and cut slits in the bottom of the cartons for drainage if you want to, or just water carefully. Then when you're done, throw them away. Save the flats and domes for next year after cleaning them up.

leava - You can still use the flats because you will need something solid to keep the containers in for watering. Most trays aren't strong enough to pick up when loaded down with containers, but they do keep things dry. My peppers always seem to grow at different rates so I shift things around so that tall and short ones are not side by side, or short ones are in the middle and tall on outside, etc. If your lights are on chains you can make one end lower than the other. I like for my tomatoes to grow with lots of light but not a lot of heat, so I try to grow mine in a cooler room once they have germinated. I also find that the shelf ABOVE the light provides the right amount of heat for germination. I have flats with dome covers that I put on the shelf above, only until germination has occured. As soon as I see the first sprout I move all of that type to the shelf below and under a light that is very low over the plant. On things that are in larger pots, I also use kitty litter pans from the dollar store like George does. It makes things easier to move outside on nice days since I can carry several containers at one time inside the pan. For wintersowing which is all done outside, I like gallon milk jugs, and I don't mind having to pull the plants apart or prick them out for transplanting because I have all of the mess outside. For my light shelf planting, I make soil blocks. I have two different sizes of soil block makers and if something doesn't germinate I just throw the block back in and reuse the soil. With new seeds I get a very high rate of germination tho. Since I plant a few tomatoes of a lot of different kinds, I use very small blocks and put as many blocks as I need onto a small piece of aluminum foil. I leave enough foil on the ends that I can pick up the whole group of blocks and move them out of the flat and to the light self once they germinate without disturbing the other blocks. I have a marker on the foil with them. When I am ready to pot them up, I make the remainder of the markers (one for each pot). I pot up after the tomato plant has it's first two real leaves. I partially fill the pot, pick up the soil block with my fingers, place it in the pot and fill in around it with soil, and mark it. Mid February is probably about the right time for me to start tomatoes. I usually plant pepper seeds at the same time, but I hold them a little longer in pots before putting them in the garden so I can make sure the cold weather is really over. In spite of careful planning, I still have to cover tomatoes some nights. I usually use nursery flower pots for covering them. It takes two per plant so I can stack them so the holes don't match up. After I have moved them outside, but they are not yet in the garden, I try to keep the tender ones on a small wagon that I can push into a building if cold weather threatens. Sometimes it gets cold enough that I have to move them back inside where there is heat, and sometimes just pushing them inside a shed that keeps off frost and wind is enough. It sounds complicated, but it isn't. It does require quiet a lot of time and effort tho. Many people seem to think you are just throwing a seed in a pot and don't realize the work and cost involved to get them ready for the garden. Of course, there is also the risk involved, because if you make the wrong decision one night and they freeze, then all is lost.

You have phrased your post as an either/or question but it isn't really. The only container a person might plant straight into the ground outside is a peat pot, peat block or other supposedly degradable pot. I say 'supposedly' because experience shows that these pots rarely work well. They constrict roots and wick moisture away from them. Unless absolutely soaked and completely buried they can dry out like cardboard and seriously stunt the plant. Search on here for many threads about peat pots. As for 'removing the roots and shaking the soil off' you don't need to do that either. You just turn the seedling gently out of its container and plant the whole root ball into the ground. Don't start shaking the poor thing about. If the roots have filled the container entirely you can tease the outer ones out gently but otherwise leave them alone.