Agreed on moisture being the biggest bogeyman coming for your seeds. I bought a big bag of silica gel packets. I put a few in each of my seed bags (I use ziploc bags to sort seeds by type), then a handful into the plastic box where I store the bags before I seal it up.
Sometimes I even drop a packet directly in with seeds before I seal them up into a plastic bag - like anyone getting any of my freshly harvested seeds from yesterday will get them with a silica gel packet, just in case.
You can save the packets that come in stuff like vitamin bottles, if you don't want to spend extra money.