I should try thinking about strategies more from a timing perspective. I do to some extent, but I don't always fully take into account how long it takes everything to get to my opponent when I'm thinking about it. Of course, for slower buildup strategies, it's reasonable to expect that my opponent will often move towards me before everything would get to them.
While I agree that there is a great deal of subtlety in each strategy, and a change from one threat to another can change the optimal counters, I think it's still useful to look at broad categories.
In your example the best cards to use as answers are different, but they're both essentially control plays, whether you're moving the creature out of the way and neutering it's attack or stun locking it. Arc Lightning and Lightning Bolt are good for preventing the Iron Golems from getting actions, but you'll end up spending a lot more than 13 mana on those cards if you want to keep an Iron Golem shutdown. Besides, that's what Earth Elemental is for.
The counters to different threats vary, but slow powerful melee creatures are generally best dealt with by control plays. They're a big investment, and it's often better to bypass them as best you can than to try to kill them. Maybe that means moving it out of position. Teleport is a good card for dealing with slow threats in general. Then you can say that if you're specifically dealing with Iron Golems, lightning attacks work well to repeatedly stun them. Darkfenne Hydra is specifically vulnerable to Force Push and Agony. So while there are specific counters that work best against specific threats, you can also come up with categories that are all vulnerable to a specific card or tactic. Maybe there are exceptions to that particular counter, but it's useful to come up with a conceptual framework and classification for strategies and threats.
As for beatdown, I think of it as something I transition into once I have my initial creature(s) up and running. Okay, I have my Steelclaw Grizzly and some Bitterwood Foxes out, it's time to buff my mage and go hit things. So while only the FM should attempt solo beatdown, it's useful to think of beatdown as an important step in many builds. It's really a timing issue. Maybe with one build I'll summon creatures and get setup for 4 turns, and then I'll transition into beatdown. In another I'll just summong Vampiress first turn and go into beatdown from turn 2 onward. Of course, getting your mage into position may take time, but it's still useful to think about when you're switching gears.
As for your issue with treating creatures as extra actions, that's why I considered my mage's actions and cards that let me cast spells (familiars and spawnpoints) in terms of action advantage, and other creatures in terms of board advantage.
On the other hand, everything you can play that gives you extra stuff down the line is less versatile than a mage action. Even if a familiar is more versatile than a spawnpoint, you can only cast some class of spells. In that sense, playing a familiar is an investment in more actions to cast that particular kind of spell, while playing a Vampiress is an investment in guarding and attack actions. I can definitely see where ringkichard is coming from with that analysis.