The default mode is always Counter + the best of the other effects for the board state
If the payment is followed by the phrase "When you do," then you'll choose any targets for that reflexive triggered ability and put it on the stack before players can take actions
However, theres an awful lot of creature cards in March of the Machine (and other sets, of course) which have two sides, as well as the aforementioned Battle cards
While one is on the battlefield, use the characteristics of whichever face is up with one exception: if the back face is up, you still use the front face's mana cost to determine the back face's mana value
This is one of several cards which has a flavorful theme that I love: An implement of torture which has a poppet effigy of the enemy planeswalker in it that transfers the damage over to the Planeswalker if they dont fulfill certain requirements
(The ranking was called Eternal at the time) I occasionally fell from the top spot, but I would regain it and stay at number one in Japan for quite a long time