I don't have much to add myself but CAP's definition of a Counter
might be worth a look for your purposes
Essentially there are six characteristics of a counter, as follows:
- Can switch into the Pokemon's strongest reliable STAB attacks at least three times from full health.
- Can switch into the Pokemon's strongest possible coverage move at least twice from full health.
- Can stall the Pokemon indefinitely using its recovery options, either forcing the Pokemon out or healing enough that the Counter can alternate between recovery and attacking.
- Can OHKO or 2HKO the Pokemon with one of the moves on the Counter's relevant official Smogon moveset.
- Can cripple the Pokemon with a permanent status move without risking an OHKO.
- Can set up, use hazards, weather, or otherwise execute an opponent's strategy without risking a 2HKO.
A Pokemon that fulfils three or more of these criteria is a hard counter, and one or two of these, a check.
Dunno how much that helps but it's suited the CAP Project's purposes thus far. It doesn't mention common battle conditions, but I'm sure you could probably add "under common battle conditions" to all of the above if it bothers you that much.