I’ve been making a lot of my own seedling soil and cutting mix for a few years now. It’s super easy to make, and you can control exactly what goes into your mix. I’m not convinced it saves money unless you make a lot over a long time, but don’t think it is much more expensive either than pre-bagged stuff.
The more you get into your own propagation, the more interested you would be to add things that may promote root growth, or enhance seed germination, or other interesting bits, but at the very most basic, you don’t need more than compost, coir and sand.
While you can change the ingredient ratio around a bit, I have found that the following recipe works really well (I do increase the sand content when making cutting specific mix):
4 parts compost + 2 parts coir + 1 part washed sand; mix well
COMPOST (forms the bulk of the soil)
You don’t strictly need to sift your compost, nature sure doesn’t specifically go make “fine” soil for seeds to germinate into, but it does help the home gardener, especially if you have small seeds.
I made a compost sifting sieve by stapling 1cm square mesh into a wooden frame, and find that is good enough to get rid of the bigger bits of bark and debris from my compost.
You can use your own home-made compost for sure! Just be certain that it is well cured.
COIR (increases water holding and soil friability)
Coir is a by-product of the coconut industry, and is simply the fibre from the outer husk of the coconut. You can buy coir in condensed bricks in most garden centres or hardware stores, and soak it to reconstitute it.
SAND (increases drainage and creates air spaces for roots to grow)
I use washed play-pit sand, but you get specialized horticulturist sand too in different sizes.