Plastic tea bags and storage

Reminder: fresh teas are best stored in a dry and cool place, without smells, little air and away from sun light.
The above blurry picture was taken from the inside of a silver tea bag like the one on the left hand picture. It shows that this kind of plastic tea bag lets some light through. This may harm very fresh and tender leaves like green tea or light Oolong. (For roasted teas, I don't think a little light won't matter much after all the heat they got through the roasting.)

Is it better to transfer the leaves to a tea box or tea jar then?

Fresh teas are meant to be drunk at a quick pace, within a season or 2. That means that the volume of tea will diminish over time. You would have to constantly transfer the remaining tea in smaller and smaller containers to minimize the air inside your tea box/jar.
Plastic bags offer a more practical way to minimize the contact of tea leaves with air: just fold the bag tightly and clip it tightly closed. And then, in a second step, put this plastic tea bag in a box to block the light.

Note: Not all plastic bags let light through. This dark green and gold tea bag, for instance, is thicker and blocks all light.

By the way, I've bought this new, professional vacuum sealer this week. It will give me more flexibility to make tea samples.