Rainwater Management

I'm placing these videos here so I can go back and reference them. We had quite a few torrential downpours this spring - wonderful for the plants, but as I watched the torrents sweep across my yard, I wondered whether I can do something to manage the rain flow a little better. Here are images from the front yard.
The water sweeps down the slope from my neighbors' property, floods the little gravel path I created and creates a puddle on our walkway. I'm thinking I could dig out the garden on the left side of the picture, build a small swale to encourage water to drain off the sidewalk. This is one summer project I plan to attempt. 

In the backyard, this is the scene. The gutters are not very effective (they might need to be cleaned out as well). But they just haven't seemed to work well since they were installed. So, right next the house we get a giant puddle. Again, I'm thinking I could dig out a swale to carry water away from the house, and down toward the side garden by the fence.