Hi! I really agree with the second part of Dmitriy's answer! With the cash back, rewards, no fee options in credit cards today, I think it makes sense to pay the monthly bills with cash back/reward credit cards. Two important points though - you need to commit to paying off the card IN FULL every month, and you don't want to use the credit card for places that charge a service fee for using credit. For example, in our town, property tax can be paid with a credit card, but a 2% service fee is charges. Also, a few companies don't allow credit cards, so you may have to connect a bank account to pay those bills.
One tip - consider a separate card for covering those monthly bills. I opened a credit card that I use ONLY for monthly bills. All ten monthly bills are on that card and I can see them and easily monitor them. For many years, I used one credit card for everything. Then a few years ago, I put the monthly bills on one separate card because over the years my credit cards have been compromised/stolen (even though they aren't lost by me!) and the credit card company issues me a new card. Then I have to go in and change the automatic payment card number at ten different places, which is a big hassle. And, if the theft/compromise occurs at the time a bill is trying to be paid, you could be charged a fee for non-payment. That happened to me once, and the utility company was unsympathetic in waiving the insufficient funds fee! You can imagine that this financial planner was MAD! I really try to keep up with money things and felt that it was really unfair that I was charged a fee for circumstances like that! I am not quite over it yet. :)
For your question about which card to use, make sure it has no annual fee and is generous with cash back and/or travel or other rewards. WalletHub has a great site you can check out to help you pick one.
Best wishes to you and thanks for writing!