Of course, Wisdom, Resistance, and Tactics are also necessary skills that will be useful for both warriors and mages.
Logistics is a very important skill (especially for Necropolis, Swamp, and Tower heroes).
And as additional skills, Attack, Defense, and Diplomacy are good choices, and Intelligence is also good for warrior heroes.
Here is a brief list of the most essential skills based on personal experience.
I can also immediately list the most useless and stupid skills in Heroes 3: Ballista, Ballistics, Mysticism, Scholar, Scouting, First Aid, Eagle Eye. Even Fire Magic can be included here... besides Berserk and Armageddon, there is practically nothing useful there, and these spells are used in extremely rare cases.
In short, if the game has given you any of the listed skills, that's very bad :( although not fatal :) and in general, don't get into the habit of having your main hero wander around witch huts without proper preparation.
THAT'S IT!!!:D