Crack in concrete slab of house - what best to fix it with?
The fact that you have water seeping in through the cracks is much more concerning to me than the cracks themselves.
I'd start at the outside of the home and find where the water management on the property is not working right.  Check your downspouts, check your grading, check especially outside the room that this concrete is in.  Solve that problem and you should resolve your moisture issue inside.
As far as the crack itself, nothing really must be done but there are tools &quot;crack chasers&quot; that you use to cut out a wider slot following the crack and then fill the now larger crack with a concrete crack filler product that will seal it up.
You must, however, deal with the water first as it will recur if you just patch it.