I love the points I get from my current cards, but what card is this actually? This sounds like a really killer card I’d use frequently for these use cases.
I've done it with a Citi Double Cash card. It's a nice all around card: 2% cash back, price matching, temporary numbers, etc. Don't take my recommendation blindly though, do your own research first of course!
Edit: As a meta-sidenote, it was very difficult for me to write this comment without feeling like it would come across as corporate shilling. I have no connection to Citi and nothing to gain from recommending their card, but there's no way for anybody else to know that, and the issue of selling old accounts is a real one (though don't know about HN specifically). I wonder what the best solutions are to this sort of issue.
Bank of America credit cards have this, they call it ShopSafe. My old Citi card had that although I can’t verify they still offer it. I believe Capital One has virtual credit card number capability as well.
So unfortunately if you get points I'm guessing you're from North America and probably won't be able to apply.
I haven't searched but there might be such services available to you in a nearer bank.