I think you give a fair explanation of Dave in this comment. I definitely think much of his “baby steps” needs to be updated. Just for example, $1000 in savings is just going to cause someone to get further into debt when an emergency comes up.
I like the 20/30/50 rule for budgeting (20% saving, 30% fun and 50% needs). If you have bad debt (consumer debt, bad auto loan, etc), then minimize your fun spending the most you can in order to wipe out that bad debt as quickly as possible. But of course also save up at least on month of needs or your largest deductible (whichever is greater). Then once the bad debt is gone save up a 3-6 month emergency fund (according to your personal risk/comfort level).
I also think it’s important to not be too hard on yourself. Some months you’ll be over budget and some months you will be under. That’s why I think it’s important, like you said, to leave some room in the budget and not get caught up in zero dollar budgeting.
Congrats on making it that far! I’m sure you’ll have a fully funded emergency fund before you know it. I hope no emergencies come up while you build it, but if they do, don’t let that discourage you!