Most effective hero?

I think it's more dependant on what items you have than class after a few playthroughs - before getting a new phone I had unlocked the huntress (by using a Rogue) and gained books on the three characters except the huntress.

I personally found the huntress most difficult to play, Warrior and Rogue were equally easy - Mage wasn't too bad either. Warrior is just an easy start due to the extra 1 Stamina.

I found that if I had a high armour of entanglement and 3-4 different battle wands I could easily get past the first two bosses on any of the three original characters.

Countering your experience my Warrior had the highest level achieved - using wands, having plenty of food (teleportation wand + piranha is an easy way to get food), and either unenchanted armour OR entanglement armour (found most other armours to hinder my gameplay but that is not the case for everyone).

I've not experienced an issue with lack of Health Pots, but when you pass the second boss or so I found my Mage, Rogue and Warrior to be rather similar in style as I would have collected wands on all of them to aid gameplay.

I wouldn't put any character above others (exception huntress but that is likely my inexperience with the character) as towards end of game you can have them built almost identically.