One card not mentioned here yet would be Sears MC/Shop your way MC... While Sears is definitely on life support, how would they line up with everything else mentioned? I'm probably going to be doing some home renovations myself in the not too distant future so I'm following this topic as well.
So far, I agree with AOD. 3% and you get it anywhere, anytime on anything without caps.
I haven't been in a Sears in over a decade (apparently nobody else has either, lol), but from what I remember it didn't really offer much in the way of home renovation stuff. Basically just tools and appliances - the appliances were the same as the ones for sale at Best Buy for cheaper, and the tools were nothing special that couldn't be bought online or at Lowe's/HD.
Maybe they carry a lot more than that though, I'm not really sure - could be worth looking into