Kyla, I'm guessing you have no cats?
Storing in paper (in a uniformly dry climate) is probably better than storing in plastic. Even very dry seeds metabolize a LITTLE, which releases humidity, which speeds up metabolism,k aging seeds faster.
Best of all would storing seeds in coin envelopes or other paper, INSIDE something that seals tight, with a desiccant packet and humidity card or humidity meter.
I store in 2x3" Ziplocs, and rely on the leaky "zipper" and diffusion right through thin plastic to let humidity out. I used to keep silica gel in every tub, but haven't refreshed it in too long!