Eventually you'll have 6 large bags which is more than enough space. Getting the hang of alchemy and gardening is pretty much the key to the game, you'll spend much more time doing that than actually battling enemies. It pretty much becomes your main source of leveling, and it's fun to boot. The idea is to always be building up your materials to 9 or 10 so you can mix 90s for the 30 phozons per potion mixed.
Some simple tips:
Mulberry seeds are plentiful and take only 5 phozons to grow, the resulting two mulberries can take a 0 material to a 10 material.
A good way to get your 9 is to use one mulberry for 5 and then a bone from an eaten chicken or lamb chop for 8, and finally a napple core or grape stem for the remaining tier.
