Sand GoblinThe overarching strategy for the game is simple. Kill your opponent, lol. Now, you can go about killing them in a variety of ways and there is no single overpowered strategy at the moment that dominates the game.
Here is a good thread regarding a bunch of the different strategies you can take. It was written very early in the game's life, before any expansions, but I think it is still very relevant.
Pretty much any mage can be played aggressively like you desire as well. Some of them are better at it than others though. As has already been mentioned, the Forcemaster, Warlock, and Straywood Beastmaster are all notably aggressive mages. The Forcemaster is probably the fastest and hardest hitting out of the bunch, but it is also probably the most restricted in strategic options.
As far as most powerful cards are concerned, there aren't any incredibly powerful cards that I can think of. No single card consistently swings the game in your favor every time it is played. Teleport probably comes closest, but that's because it can force your opponent into a dangerous situation. It doesn't cause a bad situation itself. You have to arrange a bad position for your opponent with other spells and then use Teleport to put them into that position.
Pushing someone through a Wall of Thorns can also be really powerful if they don't have any armor. Players will learn quickly the value of armor after you do that to them a time or two.
Generally speaking though, you want to have a diverse spellbook that covers a lot of situations rather than just throwing in "powerful" cards.
When teaching the game, use the Apprentice Mode rules. Once they move up to the full game, if you feel you still have an advantage over them, you can handicap yourself by adjusting Life values. That's my best advise in regards to that. I don't really have any cards to suggest for a really powerful book to give them to help balance the playing field.
ReddawnCharmyna made a tier list awhile back here which most of the forums agrees is pretty accurate. Some may change a mage up or down on the list, but I doubt by more than one tier. This discussion was in regards to the game in general and most people may have been basing their experience off of casual play and play on OCTGN, but I think it would still apply to timed tournaments.
Pointing to tournament victories as conclusive evidence that Aylin's list is wrong is flawed because of a lack of statistical data. Tournaments tend to have a fairly small turn out still yet, and don't always have the most optimal of builds present. That doesn't mean her list is completely accurate either, but I think you are dismissing it too quickly. It lines up fairly well with Charmyna's list and the general consensus of the forums.
You are correct that it seems to have a correlation to channeling, but that doesn't necessarily indicate causation. There's a lot of other things that are at play. I think the Wizard is on top because of the large and varied nature of the very useful arcane school. I think the Priest struggles because the holy school doesn't support his aggressive style very well. The Johktari Beastmaster has some identity issues with her abilities working together and working well against non-living. The Warlord has multiple problems. The rest of the mages she listed, I think should have all been listed as equals and her ranking of them seems somewhat subjective, but not necessarily wrong. They're just too close together for me to be comfortable to call, but others may feel comfortable ranking them.
In that light, channeling doesn't really have a say in the matter and the time limit shouldn't really matter.