how to manage rain water from deck?

back deck (10 x 14) has solid top and walls on most parts, deck is over poured slab. both the deck and slab slope away from house. in the pacific NW - lot's of rain.

back yard and garden bed slope towards the deck / house. drain hole is present to allow any water that might get onto the floor to drain out into garden. over time the garden had been built up and water now flows in via the drain hole onto the slab.

I want to focus on directing the water from the deck top somewhere. If I put a gutter on the side that drips the water I'm not sure how to direct the water away using a downspout as most of the yard is up hill and I don't want to direct it towards the house. I've seen pictures of "dry wells" but this looks like a huge amount of work...

It's also been suggested that I dig a trench under the drip edge, next to the foundation and fill it with stone (I'm assuming one would use some kind of fabric to keep the dirt out) to allow the water to drain down. seems this would require it to be just next to the wall / foundation of the slab in order to catch the water. not sure if that is a good idea - but that is where all the water is going now.

I plan to put more plants in the garden to minimize water coming from that direction.

Ideas? Suggestions?

Thanks very much!