I started this project in the middle of summer, but in their natural environment apple seeds germinate in early spring to catch some direct sunlight before more established deciduous trees around them start growing leaves.
If I'd stored the seeds over winter and started the germination project in early spring my trees would have also had more time to build up mass before losing leaves for the winter, giving them a higher chance of surviving their first winter.
Apples have a very low degree of parent to offspring similarity, due to both their high degree of heterozygosity and also the fact they do not self-pollenate. Any apple you grow from this method is unlikely to look or taste like the same variety as the one you obtained seeds from.
Apple seeds start out in a dormant state and will only germinate when they're cold. I folded the seeds from one braeburn apple into a wet paper towel and put them in a sealed container in my fridge.
Several days later roots will start emerging from many of the seeds. At this point they can be transferred to pots. I used compost rather than potting mix, but the composition is similar.
There is quite a high mortality rate at this point. I potted 6 sprouting seeds and only 3 continued to grow. Most of the seed will emerge from the compost with the just the base of the stem and the roots on the outside. A few days after that the seed husk will drop off exposing the cotyledons.
The sprouts that have made it this far continued growing. I planted them in the ground when they were around 10cm tall.
Putting in a stake may be a good idea. I didn't because I planted them in places where they're sheltered from the prevailing wind, but if you do so it's better to put the stake in at this stage so that you don't damage any roots, and then tie the tree to it once it's tall enough. It's best to place the stake on the side of the tree which would usually be upwind.