Glass containers work fine and come in the same shapes as plastic containers do. They are heavier and take a little more space due to being thicker, but it's a small difference.
They do have plastic lids most often, but the lid doesn't have to touch food.
Yup, the IKEA one’s are more than good enough. And they’re borosilicate so you can even use them in the oven.
The plastic issue is also why I think people doing sous-vide are insane. You’re vacuum sealing meat into plastic and then giving it a nice long leeching in hot water. Sometimes with acidic foodstuffs!
They do have plastic lids most often, but the lid doesn't have to touch food.