Fast answer
For most first Varenna stays, start in or close to the lakefront old town if the point is the classic Lake Como base: views, promenade walks, restaurants, and easy ferry access. Move toward the station edge only when train arrival, light luggage, or first-day ferry transfer matters more than atmosphere. Choose hill or Perledo stays only when views are worth steeper movement, use Fiumelatte or the south side for a quieter villa-side stay, and compare Bellagio before assuming Varenna should carry every central-lake night.
If you only do one thing
Choose the lakefront old town when Varenna is meant to be the main base and you want ferry access plus evening atmosphere. Choose the station edge for arrival convenience, a hill stay for views only if luggage and walking logistics are solved, and Fiumelatte only when the south-side villa walk matters more than ferry-door convenience.