720p, although IMO you won't notice a big difference between that and 1080i. I assume you're in the market for a new TV. Why not go for 4K or 1080p? They're so cheap now. I don't know what your budget is, but an OLED (or similar) set is worth the extra coin. I absolutely love my LG 55" OLED.
720P means progressive scan, no interlacing. 1080 is interlaced, such that half a picture is "drawn" with open space in between each "line" where at the next frame that is drawn interlaced with the 1st image (happening faster than you eye can see, but with motion on the screen you can see it). 720p is the better picture.
Only if the refresh rate is slow. Anything at 120hz and up should be fine at 1080.
I will say this, the higher refresh, the more you notice persistence of view tricks. GI Joe the movie is hilarious during the Paris scene where they are running in the exoskeletons. On a slow refresh, it looks like they are hauling tail, but on a 240hz refresh, it literally looks like they are taking a leisurely jog