Yes, you can use regular seed starter mix to start seeds that's what I use. And like OldMedUser said, you don't need to fertilize seed starter mix right away, I would wait maybe a week or more based on how the sprouts look.
Also, no need to sprout them first before putting them into pots. IMO the whole soaking until the seeds crack and then planting into the soil is unnecessary and more often than not only introduces the potential to damage roots. Most breeders these days recommend germinating directly into your seed starter medium.
Whichever way you do it good luck and have fun!