Basically was, for instance, likely to count "activities" across many computer systems and show a rollup of this activity, what can the database seem like to keep the information?

Simply this? Appears too simple. I am overthinking this.

ACTIVITYID  COUNT
----------  -----

When the volume won't be absurdly large, I'd most likely produce a table that logs each event individually, having a DateTime as @Turnkey indicates, and perhaps the equipment that drenched it, etc.

LOGID (PK)  ACTIVITYID  SOURCE  DATELOGGED
----------  ----------  ------  ----------

That will provide you with the capability to operate a query to find the current count, also to make use of the data to find out occasions currently period, and/or from a specific machine. A clustered index on ActivityID should provide you with good query performance, and also the table is narrow so card inserts should not be too pricey.

I believe the actual activity would create some form of record with a minimum of an ActivityId and ActivityDate inside a logging table. Some other column may be the identifier from the computer creating the log entry.

You would produce the count by aggregating the game records on the specified period of time.

Metro.

Yes, I am afraid it's that easy, presuming you're only thinking about the amount of occasions each activity happens. After you have that table populated, you can easily create, for instance, a histogram from the results by sorting on count and plotting.

I believe you could include a DateTime area to ensure that that you can do reviews from the occasions between a particular time interval, or at best know once the last activity count was taken.