If you want the best results, DO NOT USE PLASTIC! Use some sort of paper. I like newspaper, folded into envelopes and the seams sealed with "scotch" tape. You may want to use a double thickness of newspaper. The newspaper absorbs and dissipates any residual moisture your seeds may retain. Plastic will hold that moisture and mildew may set up. You can use an open plastic box or pickle jar for storage but don't put on the top. Also, put paper towels in the bottom to absorb and dissipate moisture. For shipping, leave them in the newspaper envelope and then make fold them in cardboard for protection. Mail them in a padded envelope.

I agree with TSmith. Give your seeds plenty of room to breath and dry out. Never use plastic.

No plastic? I don't think so.
Depends on the seed - if they require moist stratification, plastic is fine - I've been stratifying acorns, nuts, persimmon, pawpaw, and other seeds that need cold, moist stratification in ziploc bags with some moist newsprint, paper toweling or peat for decades.
If they're seeds that don't have to be kept moist, paper may be OK, but if they are seeds like those listed above, attempting to store them in anything other than a plastic bag or a tightly-closeable jar or plastic container will result in them dessicating and most certainly being non-viable come spring.

We harvest our Daylily seeds in the late Spring as the
seed pods begin to dry out. We then place the seeds in
a jar or plastic baggie and put them in the refrigerator
(not freezer). We plant them early the next Spring.
Have had great success with this method.

THANKS, for all the information! It has been very helpful.
Viv