Some notes / tips I made for myself for when I replay AP again someday:
Notice that spell power scales with INT, with extra bonuses every multiple of 7 (INT = 7, 14, 21, ...)
Don't trade runes in Monterro. You might have too many X now, but you'll need them later.
Troops:
Inquisitors are the only way to resurrect level 5 troops. Casting Phantom on your Inquistors is one way to resurrect level 5 if you've already used the Inquisitors' one charge.
Your dragon:
Crushing blow's knockback is a way to keep an enemy troop away from yours while you work on its fellows
If the enemy is no longer a threat (no hero casting spells, troop has no ranged attack or is almost dead), use any rage to dig up treasure (it can rarely even be a rune). Wake Dragon will let you dig up 2 chests in one turn.
Skills:
It can be better to get level 3 of 1 skill than 3 x level 1. For example, the attack and defense skills go +1, +3, +6. So level 3 is +6 while 3 separate skills might all be +1.
Neatness level 1 is great, especially if you are a mage, but it will only give you crystals. Level 2 is also worthwhile later on since there is a lot of level 4 gear and some of it gives you 2 runes instead of crystals. Don't destory anything without the matching Neatness level or you'll just get a lousy 1 crystal.
Alchemy: get Neatness instead.
Holy anger is very useful later in the game since you'll face a lot of demons and undead. At level 3 their attack is -15!
Work towards Higher Magic as soon as possible. It will let you dispell / heal + attack, or do two attacks like Fire Rain + Geyser
I found Rage much less useful in AP as a mage, so I would fill out the mage skills and other mind / might skills before getting the Might rage skills.
Items / Gear:
Some gear sets have very nice bonuses, making them worth collecting even if one set item isn't worth using by itself. BUT: gear is randomized, and you may never find all the pieces of a set.
Spells:
Pay attention to mana cost of higher-level spells, for a few (heal, fire arrow) the cost is constant or even goes down. And level 3 heal also cures poison.
Remember you can use level 1-2 versions of a spell even after you learn level 3, with shift and control keys.
Teleport is handy if you're fighting demonesses.
Trap can stop any (non-flying?) stack for a turn, and block anything behind it. Like the dragon's crushing blow it can buy time.
Clam Rage spell is great for non-hero boss battles (Driller, Spider,...) since you can't use your dragon in them. Phantom is also very useful against these bosses.
Favorite opnening attack: (Fire rain or level 2 ice snake) + Geyser.
More on Spells:
Geyser - essential tool for whittling down enemies, at level 3 you get 8 strong attacks out of it (if 8 enemies). Very useful for upgrading / suppressing items.
Healing - cost goes down at higher levels, level 3 also removes poison / plague
Fire arrow - damage and % burning grows, cost does not
Poison skull - good for anything that resists fire, poison chance is 100% at level 3
Later:
Teleport - get Demoness-teleported units back to safety, move a slow tank (knight, paladin, ent) into range of an enemy ranged unit
I think the penalty to leadership in comparison to the warrior class is completely unbalanced towards the mages magic benefits. 
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