Always think layering. We are leaving in a day for a hiking trip, been checking the weather and looks to rain every day. I am packing a fleece jacket, long sleeve shirts and a light down vest. On colder days I'll wear all these items under my rain jacket. If weather gets warmer, I start peeling off layers, down vest first, then keep going as necessary.
A down vest or a fleece jacket is your best lightweight layering piece for under a rain jacket IMO.
A few years ago I purchased a long rain jacket for city wear from Kuhl...https://www.kuhl.com/kuhl/womens/outerwear/ws-jetstream-trench/?color=Blackout I've worn that layered over a long (costco) down packable jacket that is about 10 years old now !
And as another poster stated, bring a ball cap and wear that under your rain hood so you can see ! The brim will keep the brim of the hood out of your eyes and makes the jacket work that much better.
PS> I always pack a small umbrella too... came in very handy touring Stirling Castle when the drizzle just wouldn't stop