I'd put them in a well-labeled cardboard box. A kitchen size matchbox should hold plenty of primers. Don't worry about desicant, just keep them inside the house. If the environment is good enough for you, it's good enough for primers.
Next time leave them in their original packaging (trays) and dry the whole mess together!
Never a glass jar and I wouldn't use plastic either. Nothing that will throw off shards if the primers were to detonate. Don't make a habit of dumping all the primers together for storage. They are separated in the original packaging for a reason.
Proud member of the NRA and Texas State Rifle Association. Registered and active voter.