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Gamepad-friendly is the non-compromisable item here. I use a keyboard and mouse a lot at work, and a keyboard a fair bit at home. If I play games at home that require aggressive mouse usage, I'll probably hurt myself and be faced with the choice between quitting the game or quitting my job. And I'm not going to quit my job to play a game.
A game that can be played mostly using the keyboard with a little bit of mouse usage is plenty good enough. Gamepad buttons can readily be mapped to keyboard keys. Combinations of buttons can also be mapped to keys, so needing 30 keys probably isn't a barrier unless a game's control configuration options are awful, such as a lot of controls being hard-coded to particular keys and not changeable.
Games where you have to constantly use a mouse are out of the question, though. Mouse-optional is fine, so long as mostly gamepad is also an option. But if it's hard-coded in that you always attack in the direction of the mouse pointer and there's no way to change this, that pretty much rules out the game unless it's very slow-paced.
For a game to offer built-in controller support is not necessary, nor even desirable. Built-in controller support virtually never works right out of the box, anyway, so I usually end up having to disable it in order to use a gamepad.
What I'm seeking for combat is basically interesting combat. Start a battle, sit there and wait for the mob to die, and then collect your loot is not interesting combat. Twitchy action combat is probably the easiest way to make interesting combat, but not the only one. A game that requires complex, varied strategies works, too. Standard trinity combat is not complex or varied strategies, nor otherwise interesting.
I'd like some challenge to the combat, too. If I seriously screw up, I should die, or at least have to frantically flee for my life. Challenge that consists entirely in assembling a group does not constitute challenging combat. Combat that does not become interesting until after months of grinding for levels is combat that is not interesting at all.
It's essential that a game be released and at least somewhat polished. Game X that doesn't release for two years and may or may not fit what I want is not useful to me now. Game X that has a Kickstarter and is probably vaporware is even worse. I'd like a game that I can reasonably play tomorrow.
I have been able to find some games that offer what I wanted. I'm basically hoping that there are others that I simply missed. Spiral Knights has the best combat I've seen in an MMO, and by a considerable margin. I liked Guild Wars 2 and Champions Online, as well. Going further back, I liked Guild Wars 1, as well as the ship combat in Pirates of the Burning Sea. I did like A Tale in the Desert and Uncharted Waters Online, but for reasons having nothing to do with combat, so those aren't really predictive of what I'm looking for.
I'm fine with a game being AAA or indie. I'm fine with it being recent or older. I'm fine with 3D or 2D, as I'll overlook poor graphics if the game mechanics are good, but I do want a standalone client and not browser-based. I'm not okay with involuntary PVP unless there are compelling reasons why I won't be attacked very often. I prefer subscription, but can accept some "free to play" models, so long as they don't become aggressively pay to win. (Loose definition of pay to win: someone paying $50/month is at a big disadvantage as compared to someone paying $100/month)