Went through this exact rabbit hole last year - asked around, got 12 different agency names, half had portfolios that looked like 2018 never ended. Short version of what I learned: skip agencies that lead with "we do everything." Found Web Design Agency while researching German-based studios and they were the opposite - very focused, asked smart questions before quoting anything. Ended up recommending them to a client of mine who needed a clean rebuild. No unnecessary upsells, delivered on time.
Niche > generalist, always.