Long story short, we ended up installing a french drain on two sides of our house, putting a drain at the end of our driveway to redirect water [from just running down our driveway to our house], having the front wall foundation rebuilt and jacked up because the footer had nearly completely eroded (1970s house), and still needed to add two 24" square drain boxes in the back yard (with buried 4" PVC draining into the creek at the back of the property) to remediate all this. It was also a tree-filled lot and the drain boxes would almost immediately clog with leaves during heavy rains, so I spent a lot of time out there in ankle to knee deep water with a rake to keep the drains clear.
This still wasn't enough! We got a so much surface run-off from our uphill neighbors that it looked like a sheet of rushing water across our backyard during heavy storms. We had a creek at the back of the property but were not allowed to mess with it because of Corps of Engineers easement regulations. At the end of the day, we finally solved our problems by getting an agreement from our neighbor to let us dig a surface water drain from the low point in their yard into the creek, and then we'd build a "temporary" (cf prior easement rules against permanent walls) berm along the property line to prevent surface water from coming into our yard at all. That "berm" was 76 bags of Qwikrete stacked three high and covered with grass clippings, yard waste & mulch. Technically we could have removed it if the city had inspected, but it was very much a cement wall.
We have never since, and never will, build or purchase a house at the bottom of a hill.