I use #0 craft envelopes (coin envelopes) to store them, as they breathe and lets the seed dry more if they haven't dried enough. Lots of people use small plastic zip-loc-type baggies, but you have to make sure the seeds are very dry. Some seeds can't take dry storage (jeffersonia, sanguinaria, etc.), so you have to keep them moist, so a moist paper towel in a zip-loc is probably a good idea (I personally don't like to mess with these ones, because it's too much bother).

Most seeds won't require warm-water soaking when sown. Probably all don't, really, but with some you can help it germinate by soaking, or nicking, etc., like sweet peas (soak), some irises (nick and soak), moon flower vine (nick and soak), etc.

I also was using the #0 coin envelopes to save most seed.
I always keep a few in my purse & in the car for new finds.
I found a site that has free printable envelopes that just need to be cut & glued together.They have cute designs & are very easy. Hope they work as well for you. Enjoy!

Here is a link that might be useful: free printable seed packets