Health coverage after losing my job: marketplace or Medicaid? (update)

I have 3 weeks left on my current insurance and I am comparing options. There are 3 people counting on me, so I am trying to be careful. I do not want a gap in coverage. How fast did coverage start?

Thanks for writing this out. I went through something close to it 3 months ago, and it settled down once I kept a simple log of every call and form.