Build a wooden terrace. Then you can confidently do without a gutter and slope.
Yep... this total sealing of properties with stone and paving is really not nice.
With heavy rain and wind from the "right" direction, slope and gutter won't help you much either. Especially since the water in the corner can't flow away to the side if the wind comes from ENE.
And the children can also put something round on the wooden terrace without everything rolling into the garden. In midsummer you can't walk barefoot when the sun is shining down. In winter... well, everyone has to decide that for themselves...