Here's the ultimate question, and one I challenge.
Step 1 of a grand in your savings is great, but a grand doesn't pay all of my bills.
I think 3 months worth of your bills is an absolute minimum. Call it a waste, but if you need it, it's good to have. If you have 2-3k in monthly bills, then you'd want 10k. That's money that also enables you to jump on good opportunities (cheap car that's worth more etc).
Anything after that, I'd throw at bills/finances that need to be paid down and/or off.
It's a psychological play more so than a practical one. So is the order of the debt snowball (smallest to largest). His theory is accomplishing the goals (which are easier towards the beginning) will motivate you to keep going.