I'm a little of all three but am now an arcade player.
I started out as a chess player, to learn units and formation strengths and such and to react with detail and learn the strength and weaknesses of units.
That and to look at the cool skins...
But once that lost its touch and I started to learn the units I became more of a basketball player where I'd pause in order to rally and organize parts of a battle that got out of control.

But after playing Multiplayer, pausing just seems so wrong.....so I hardly ever pause, unless I'm in a seige battle, which makes it necessary to pause with all the path finding issues and such.

I voted Arcade, FYI.