The purest form would be a game that had elements of all the games you listed. That would be 8 ball.
At times, you use one pocket.
At times, you run down to the 8 and out like straight.
At times, you use banks to get what you need.
At times, caroms/combo's give you shot opportunity when there are no standard type shots.
At times, the CB has to go 3 or more rails for positions.
At times, you have open up clusters or move balls to where you want them.
At times, it is the safety battle that is the key part of the game.
8 ball played by those that truly understand the game is a battle between two people. It is all out war.
It is also the most game played by the general pool playing public. Do not let this fact take away from how complex the game of 8 ball is.