In older houses here that would be covered by a tall baseboard, then a line of quarter round at the bottom of that and resting/nailed to the floorboards,

I had some unsightly gaps in my house too and as @colleenoz stated, I used a wide board, trim molding then quarter round to cover it up.

Note: I typically do not like quarter round on the bottom, but here it was the lesser if the two evils. Had i not used it, I would have had to redo the flooring as it did not match up with the wall.

With old houses they typically used a 8 inch board nailed to the wall then a base board cap molding. No quarter round like what is used in this picture.

build it out with trim, or Build it out with a border tile.

6 of one half dozen of the other.

Kinda depends on your skill level.

Baseboards