Your favorite hero...

If we exclude the overpowered heroes from the campaigns, then it's roughly like this:

Inferno Nimue
Dungeon Erin
Sylvan Dyraell
Stronghold Haggeh
Haven Axel
Underworld Helmar
Academy Ora
Necropolis Lucretia

While not all of them are the strongest or most overpowered, I don't always aim to choose such heroes.

It all depends on the map size and the opponent.
Inferno On a small map, Daleb; on a large map, Nimue.
Dungeon On a small map, Leto / Synitar; on a large map, Leto. Erin is generally not a good choice.
Sylvan On a small map, Ossir; on a large map, Wingael / Anwen.
Stronghold On a small map, Haggeh / Tilshek; on a large map, anyone except Argath.
Haven On a small map, Dugald; on a large map, Axel / Mive.
Underworld On a small map, Inga / Karli; on a large map, any dwarf except Swei with a mentor + Inga.
Academy On a small map, the one who casts fireballs / Hafiz; on a large map, it depends on the opponent.
Necropolis On a small map, it doesn't really matter who; on a large map, Lucretia.