Hi Jamie;
Welcome to Permies! I hope you enjoy the forums.
Here is my take on seed starting:
Use soil. You'll often want to use a fine soil on top for small seeds, but I've never used soilless seed starter or sterilized soil for starting seeds. Mixing
compost, garden soil and sharp sand makes a great seedling mix for me. Throw in some organic fertilizer such as rock dust, greensand or some other well balanced mix of goodies, and some coir for water retention if you like, and you'll have a great mix.
I think people generally start transplants in small containers and then transplant into larger containers because of space constraints. When I start my tomatoes, peppers, celery and parsley inside in early spring, I don't have much space so I start them in small blocks (I use soil blocks for transplants), and then I pot them into bigger blocks when it's warm enough for them to go into the greenhouse where there's more space. I start them all under lights, as the lights give off the heat that they need for sprouting. And many seeds need the light to sprout properly.
For cucumber and squash, and other seeds that are started later in the greenhouse, I start them in the blocks they'll stay in until they go into the garden. And it's worked fine for me!
I'm sure other's will have their own experiences to share. So take all the info you can, and work out what will work best for you in the space you have.
Good luck, and I hope your first seed starting adventure is a success!
Cheers
Tracy