Water runoof drainage help please!

Hi All;
I live on a block where the back yard slopes downward towards the house. The previous owners have built a raised garden bed upslope of the house, and during quite heavy rain yesterday, i noticed that water runs down the hill, runs along the raised garden bed and gets funneled between the house and the garage. Now it's quite a large amount of water, and quite nearly flooded the downstairs part of the house as there was a blockage preventing the water flowing down the driveway to the street.

Now, i want to install some drainage so it doesn't happen again.

The option i have come up with is installing some drainage channel things from bunnies and running the flow to a drain nearby.

Would a better option be to direct the flow through a slotted ag pipe?
If so where do i put the pipe?
Are the flexible pipes better?
Should i get the one with the sock on it?
What else would need to go into the trench with the pipe?

Thanks
Simon.

My initial thought would be to use a drainage box channels with larger pits at strategic points. The type of trench I"m thinking about is the plastic C sections about 100 x 100mm, with a slotted removable top. While they are not that attractive, they do have some advantages. They take up and move water very quickly. Larger pits will also help with absorbing fast supply of water. The other big advantage is that the removable top means they are easily inspected and cleaned. If this is water off a garden bed, it may have sediment in it. A slotted pipe will slowly lose efficiency over time, and is more difficult to fix, if it is not operating at optimum flow rate.

You could use a combination of the two methods, the box channels where you need to make absolutely sure no water gets past, and the slotted pipe where the route is windy and you can dig it up easily. Don't forget that any slow point (eg a small diameter ag pipe with a bit of sediment) will cause the water to back up through the whole system.
Cheers
Justine

Yep have to think Justine has it squared away with this one. This method could also save the effort of digging a rubble pit. We had to install storm water run off not long after we moved in to our home. Problem we had was 50 years of water running under the house and eroding a fair bit of soil from around the stumps. Next job i have is to fill around them with a bit of top soil.