Severance offer, what should I ask for? - what worked for you?

The company sent a severance agreement with a release of claims, and I am unsure what to do. I have been trying to stay organised about it. It includes health coverage for a couple of months. What did you ask for?

Thanks for writing this out. I went through something close to it 5 months ago, and it settled down once I kept a simple log of every call and form.