Kevc, seedlings are like new born babies they need TLC, too much of everything can kill them. Too much heat, cold, water, too rich a compost and in some cases unsterilised compost. I use my own mix of seed compost 1/3 compost 1/3 fine grit 1/3 washed sand. The potting on compost is only 1/2 compost 1/4 grit and 1/4 washed sand. An old fork to get under the seedling and lift with plenty of compost attached to the root system, with my potting on tray ready filled with compost and firmed down just a little (do not compact it) poke a hole in the compost with pencil or prodder and ease the seedling into the hole but sink it so part of the stem is also in the hole then gently firm the seedling in. Water trays or pots from the bottom up (stand in a bowl of water until the top of the compost looks just damp) stand aside to drain excess water and then put in a light warm place out of direct sunlight at first and out of cold air flow. Turn the trays daily so they grow evenly and try to make sure the warmth is fairly constant at first, they do not like big variations in temperature.
It all sounds a bit time consuming but you get into a rhythm when potting on a lot of seedlings, I put my music on, brain out of gear use a high stool to sit at my compost filling tray dreaming of a lotto win, time flies.
One thing to remember some seedlings will fail and you will not need all you manage to strike, discipline is needed to just pot on what you need plus a spare tray then the rest onto the compost heap.
Hope this helps,