As a DM, I'm definitely most of the above:
Powergamer--I like to give my players challenges when combats occur, but most players complain if they feel their characters are being nerfed. Especially with how easy 3E makes it to customize monsters, I like to buff up major encounters somewhat (random encounters and mooks, otoh, are standard cannon fodder--PCs should act and feel like the Heroes of the Story).
Butt Kicker--Every great gaming session has a good, challenging encounter providing the players a "time to toss the dice." Combat is not the focus of my game, but it is a definite part. I do like cinematic combats, though, with various dramatic devices employed to increase the tension.
Tactician--Players are rewarded for smart or creative ideas, and the ex-1E player and myself enjoy teaching the "newbies" the tricks of the trade. Monsters of at least average intelligence will use basic, effective tactics in combat. Genius monsters....heh, just ask my players. >=)
Storyteller--I love politics, intrigue, and tying together seemingly-unrelated modules into one epic storyline. I'm also very quick at grabbing opportunities presented by the players (even minor actions, like visiting a tailor--it sure surprised the party when they showed up at the bar to grab the guy who hired assassins to go after them and found the assistant tailor--who had expressed such a friendly, helpful interest in them from the beginning--waiting for the main assassin to show up and collect his pay) and smoothly weaving them into the storyline. If players wish to sidetrack from my "planned" adventure and develop their characters, I strongly support (and heartily enjoy the antics that often result). I love giving out magical items custom-tailored to fit a PC's idiosyncratic style, and encourage and provide opportunities for PCs to accomplish personal goals.
Method Actor--Even "throwaway" minor NPCs often end up becoming recurring characters due to how much the players enjoy the way I've developed and portrayed them. A great session also has at least one solid roleplaying portion to it, whether a social event with political overtones, investigation of a mystery, a rigged drinking contest to impress the orcish pirate, etc.
Rules Lawyer--When I got the 3E rulesbooks, I sat down and read them cover-to-cover. I then made up quizzes (yah, my bachelor's was in education, go figure) to reinforce the rules and show which ones I needed to review. I've got cheat sheets with most-referenced rules on them, and re-review the rules every few months. As a result, my players have both a solid foundation on which to base their actions (being able to figure out the likely consequences of said actions) and complete trust in my fairness so that they don't argue with my calls, especially when an ambiguous situation arises that requires me to stretch the core rules.
Other Aspects--I also like to throw in a good, thinking puzzle every session. There are frequent moments of humor, but these are counterbalanced by tragedy, horror, and that satisfying sense of vengeance that comes from taking down that NPC villain who has outsmarted you for the past ten encounters (which brought about the counterbalancing emotion of frustration, hehe).
In short, given all of the above qualities (which I hope come off as sounding helpful, and not boastful), I would classify my DM style as:
Deck of Many Things
(Oh, and I am definitely NOT a Casual DM. I had been DMing for 10 years before I ever got to play a character of my own.

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