Would it be better for me to put my Emergency Fund into a Savings or a Checking account? I already have a Savings and Checking but I would like a third account so that I don't touch the money except for bills and it will hopefully be a short-term budget.
I wish everyone I had talked to over the years was as responsible with the placement of their Emergency Fund as you are. As far as the savings or checking discussion, both work well as your Emergency Fund. The key is to have penalty free access to the emergency fund when needed, but not such easy access that you are tempted to dip into it for non-emergency situations. So, it's up to you. If you feel you would be less tempted to touch the emergency fund by putting it in a savings account than a checking account, you have your decision.
I do have a question on the "except for bills" comment. If you are referring to emergency bills that are not part of your regular budget, then that is exactly what the emergency fund is for. However, if you mean that you are using your emergency fund to pay part of your daily living expenses, then I advise you to work out a budget that allows your expenses to be less than your income. That should help keep your budget balanced. If you are using the emergency fund to live beyond your income, then that emergency fund will eventually run out, which can lead to credit card debt.
Thank you for reaching out and for asking such a great question.