Easy on the foam. Fire hazard unless you put a retardant on it. You would not like your whole system (recording, instruments, even your house) on flames, do you? Foam used as bedding are not very good acoustic absorbers. Acoustic foam (a little expensive, not available here) are the ones to use. But then again you have to fire retard them. Egg trays are never acoustic materials. Your understanding of the present day egg tray and the ones used long ago are totally different. Egg trays do not have appreciable absorptive coefficient usable for acoustic purposes.
To sound proof, you need mass. Or series of constructed panel materials arranged as a sandwich. To tame the frequency of the room, you need absorption, diffusion and reflection.
To save money, make sure you get in touch with somebody who understands acoustics. There are several acoustic consultants around. It will save you a lot of trouble.
FWIW