Berries are shallow rooted won’t be an issue next to house. Bababerry raspberry is highly rated for so cal. Trailing hybrids like Logan , boysenberry and marionberry did well for me in 9 b norcal

If the location has hot, sunny afternoons/evenings, make sure to select caneberry varieties that do not suffer from UV damage to the fruit. Thornless Logan and Boysen (thorny; I was not impressed with thornless Boysen) would do fine. Avoid Triple Crown due to UV damage. Black raspberries would be OK. You may need to prune off any fruiting spurs touching the house to avoid staining.

It faces west and gets about 2-4 hours of direct sunlight depending on winter-summer, but rest is dappled and indirect light. I've never seen black raspberries - do they taste different? Would red raspberries not work? The Logician LLC(USDA8b-OregonPDX)

I grow boysenberries on a wire trellis along a block wall fence. They're on a north facing wall, so get mostly indirect light except for a few months in the summer. Access on both sides is not an issue because it's easy to pick fruit from one side.

All caneberry varieties would work at your location, given that smallish amount of direct sun. Black raspberries do taste different, but most people object to the seeds. Red raspberries spread aggressively via root runners.