I always start with 2 bottoms, 2 tops and one layering piece (like a cardi) in colours that go well together for every trip I make. I actually don't stick to neutral colours because it's so boring and I usually get frustrated with it after a couple of days.
I also pack a smart coat or jacket with a matching pashmina and two pairs of comfortable yet smart shoes. That is really my minimum, even if I only travel for a weekend. I built the rest of my travelling wardrobe from there, adding tops, bottoms and layering pieces that are easy to mix and match. I only wear natural fibres so I usually can wear pieces at least twice before washing. I'll handwash some items during my vacation or put them in the washing machine if we stay in a self catering appartment. Or I'd let the hotel clean them, which will probably be cheaper than paying for extra weight on the flight.
In Europe people tend to dress a bit smarter than in the US but we don't "dress up" that much. I think that the concept of dressing up or down is very American. You won't see many yoga pants or athletic shoes on the street, but you won't see many women in LBDs in restaurants, either. It's no problem to wear your (smarter) day clothes to go dining, except perhaps if you want to visit a Michelin-rated restaurant. So that should make packing light easier.
I hope that helps.
