Hello everyone,
I am sharing one of my favorite visualizations of how to put your money to work. It's from the reddit.com/r/personalfinance wiki.
This is after you budget your normal stuff like rent, food, vacation, etc, and also after you build up a Financier month buffer (you're assigning all of your income to the next month).
Here is a slightly more complex version of this visualization. (https://www.reddit.com/r/personalfinance/comments/4gdlu9/how_to_prioritize_spending_your_money_a_flowchart/)
I would put the Company match in your 401k ahead of an emergency fund.
A lot of people consider an emergency more important to have readily available, and thus more important than the match.
But you're right to a certain extent. I would prioritize a smaller emergency fund, or even just a Financier buffer, before the match, and then 401k match, and then the rest of the emergency fund.
Totally depends on the situation though. It is free money. :)