I don't do a lot of container, but I am also not a fan of peat moss. Its only function is water retention so there are mixes that are 1/3 peat moss, 1/3 sterilized garden soil and 1/3 compost.
A better mix is just half and half compost and sterilized garden soil. It has to be light and fluffy compost tho.
When I was a kid we started our small seeds like tomatoes, peppers, cabbage etc and my mother had a large number of house plants She sent us kids out into woods to collect what she called woods dirt. It was found in low places where leaves collected, pull back the leaves and there would be a two 3 inch layer of black compost between the top leaves and the plain soil. Worked like a charm for both starting seeds and her house plants. Now that I am old and lazy, I just buy a sack of Bacto mix to start seeds.