What are the recommended credit cards for big household purchases?

Very unlikely. The bonus rewards that New To Bank cashback cards can give you often pale in comparison to the sign up bonuses in terms of miles that you can get with a new miles card.

If aspiration experiences are what you wish for, then a good miles redemption will probably be worth more than oversized bonus cash back, assuming equal spend. For example, when it was launched, the SCB X card would provide one with 100K KF miles upon spending $6K and paying the $695.5 annual fee. Even if you redeem the KF miles at face value (please don't), that is worth at least $1000, or a 15% cash back on what you spend. I have not seen any card give that level of cash back yet, and most cash back cards do cap your cash back amount.

If you are already doing miles, you will probably want to stick to it. Just my 2 cents. Just be vigilant and watch for good sign up bonuses or occasional bonuses for existing cards.