That's a good plan, but OP is specifically asking about building credit.
If they know that they can afford to pay off all of their expenses, then using a credit card for all expenses and then paying the credit card off at the end of every month (which can be set to auto-pay) is much more effective.
If they don't know that for certain, then having (for example) one or two small, consistent bills per month on the credit card which they know they can pay off and which they have set to auto-pay would be a better idea.
Ideally, OP would have a credit card which offers some accumulative benefit (for example, a card which gives you points to spend on travel). That benefit can help offset any expense that using a credit card garners, such as if there is a 3% fee for paying a bill with a credit card (common because this is what Visa charges merchants to process payments).
Ideally, you would not use credit cards explicitly for emergency purposes because this will not help you to build credit, will mean that you are only using your credit card when you can't afford it (this is how people get trapped in CC debt), and your credit limit will not increase. If you truly want to have a credit card on hand for emergency purposes, you want to build up your line of credit (through regularly using and paying it off) so that you can actually manage a significant expense if/when the time comes. It also gives the added benefit of having higher credit available to you (without using it all), which is good for improving your credit score.
Also, better credit cards (which require better credit to obtain) have better benefits and these can become pretty significant over time, whether it's in the form of points you can spend or other benefits you might get such as customer service which actually does go out of their way to help you when any sort of issue arises.
Also, you cannot do a chargeback on a debit card. If you get scammed or otherwise taken advantage of financially while using a credit card, you can get your money back. You cannot with debit/cash.
I grew up being told that you should avoid credit cards at all cost and the advice was bad. Avoid credit cards if you cannot afford to pay your bills or if you know that you are someone who will overspend.