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I would try a waterproof paintable caulk
DAP makes a concrete filler and sealant that is waterproof
You can add waterproofing on the inside using caulk or special concrete filler. However if you have significant water coming in you need to address why the water is coming toward your house (drainage, gutters, etc., should all move water away from the house). You probably also need waterproofing on the outside of the house. This is done by removing the dirt against the basement walls and waterproof it. You may also need to add more foundation drainage, which can be done while the dirt still removed.
You need to keep an eye on that crack. It could mean the ground is shifting.
Do not use caulk. It will not work or last. You need to use hydraulic cement. It expands as it dries to fill and grip the crack. Follow label instructions.