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This is my path to get 270+ coins on World 1-1. My best run is 271. I mistimed my jump at 0:36 and didn't get to kill the first koopa which would've yielded the last coin.

275 is likely the maximum possible score, but you would have to play as Yoshi to jump backwards far enough to kill the two goombas on the ramp without bubbling, in which case you can then bubble back to the previous 3 goombas and combo kill them. Doing so would give you 5 more coins than killing them earlier, but the amount of time it would take to bubble back that far would prevent you from getting the question block below the star.

Why Toad? Simply put, Toad enables you to get 5 more coins than Mario due to Mario not getting any coins from the first mushroom of the level (it makes him bigger instead). Since Toad only has one size, every mushroom yields 5 coins including the first one.

I have not purchased the full game so I have not unlocked Yoshi to attempt a better score.

Credit to oho41 for coming up with parts of this route!