By the mean?
Most statistics are useful if you take the same number of measurements (IOP exams) each day at the same times each day. Your chart shows IOP exam times like 9:53, so I doubt you are doing this. (I don't do it either.)
However, if you do not do the above, you could accomplish the same result if include only a set of pre-defined measures in your mean. Don't pick the measures you like best each day. Follow a pre-defined method. Decide which IOP exams will be included for your daily statistics and stick to that definition each day.
For example, you could use your "upon awakening" IOP, your "before lunch" IOP, your "after workout" IOP and your "bedtime" IOP to calculate your mean (and other statistics such as range or standard deviation) each day.
Those IOP exams should be done the same way each day. Don't miss any of these IOP exams or your statistics for that day will be biased. (If that happens, either exclude that day from your trend, or include it but add a note that is may be biased.)
By the fraction within the target range?
Same answer as above
By the max?
Yes, this is meaningful.
By one key IOP exam each day?
This is very similar to "By the max." For many people it could be sufficient to follow the trend of the "upon awakening" IOP. Or, if you have identified a consistent time of day when your IOP peaks, create a trend chart of this specific IOP exam over time.
By the daily range?
It is important but it does not distinguish between an increased range due to elevated IOP vs one due to reduced IOP.
You can find more ideas here:
What methodology should I use for self-tonometry to detect if there is a difference in IOP between two different glaucoma medications? | Ask FitEyes