The best way to store selected seeds is to keep them first of all in paper, as this can wick water away. I tend to use mushroom bags that are available in supermarkets.
Having popped the seeds in the bag, and labelled them well (we always think we will remember, but never do) then add a sachet of silica gel. These are the bags that fall out of the box when buying trainers, handbags, shoes etc. If you pop them in the airing cupboard it will make sure they are dry.
Then store the seeds, labelled in their paper bags with their sachets of moisture grabbing gel in the fridge.
Seeds are best stored cool and dry and I have found this system works well.
Make sure you label them as seeds or pop them in a sealed container so they are never confused with something to eat eat by ravenous teenagers.