Strongest early-game counters for a Modern deck?
It all depends, I suppose, on your precise definition of "early game".  Most people would probably agree that the best counter in Modern is Cryptic Command, but at 4cc that's not anyone's idea of "early disruption"...

If you really want to come out of the gates countering, you'll want to be looking at 1cc and 2cc counters.  At the 1-drop level, Spell Snare is probably top of the heap, because so many good, fast decks will lean heavily on good 2-drops.  Spell Pierce might fit the bill if it's not fast creature swarms you're most worried about; or Mana Tithe if you want something a bit more off-the-wall (and are capable of making white mana)!

Beyond those, 2cc counters are the "classic" option.  Mana Leak is better than Rune Snag in the early game, which seems to be what you're worried about; and then there's the excellent Remand, which, while it doesn't make the problem go away permanently, hopefully makes your tempo problems go away, until you can, as you say, "take control of the late game".  Both Mana Leak and Remand are non-negotiable solutions to the problem of an opponent overrunning you in the first few turns of the game, and those'd definitely be my first port of call when working out a solid base for a Modern counter-heavy deck.