When I was growing and selling herbs commercially, I had zillions of seeds to collect and store. I don't think keeping them in plastic is a good idea, because most seeds have moisture in them, and keeping them like that causes them to sweat and ultimately to rot, especially in warmer weather. I continue to keep my seeds the following way:
I make sure they are totally dry before storing them. Collect them in the morning, after any dew has dried off. Then wrap them in pieces of aluminium foil. Then put the foil package in a paper sachet, labelled with name of seed and the date of collection (or just tape on a paper label). Then into a glass jar, which is kept in a cool, dry, dark place. If the seeds are from plants that need a long winter or cool temps before they'll germinate, they can be kept in the jar, in the fridge. If you use the paper sachets, you can also write on any special instructions for germination (needs scarifying or stratifying, needs light, ideal temps etc). The correct name of the seeds is important, of course, but so is the date of collection, because each seed-type has its own viability time, after expiration of which germination cannot be relied upon.
I make sure they are totally dry before storing them. Collect them in the morning, after any dew has dried off. Then wrap them in pieces of aluminium foil. Then put the foil package in a paper sachet, labelled with name of seed and the date of collection (or just tape on a paper label). Then into a glass jar, which is kept in a cool, dry, dark place. If the seeds are from plants that need a long winter or cool temps before they'll germinate, they can be kept in the jar, in the fridge. If you use the paper sachets, you can also write on any special instructions for germination (needs scarifying or stratifying, needs light, ideal temps etc). The correct name of the seeds is important, of course, but so is the date of collection, because each seed-type has its own viability time, after expiration of which germination cannot be relied upon.
