Any wide-mouth jar will do. (trust me, I'm Korean). BTW, the brown container in the pic looks like the fermented soybean paste. They also sell the red containers of chili paste. I highly recommend both to kick-up the flavor of your soups or any other dish. You haven't lived unless you've added a spoon full of red chili paste to your top ramen!
I would use the Ball or Kerr jars or even reuse a glass mayo jar. It's not an exact science. However, since you're making it from scratch, you may as well go large! Some people cut up the Chinese cabbage or daikon radish so it fits in the bottles. Expert-level is to leave the leaves whole but that can be messy when pulling it out of the jar to eat it.
Oh, and cover the jar opening with saran wrap before screwing the lid on. It will keep it from smelling up your fridge. Also, it may bubble up as it ferments...be forwarned.. it's all good.