Different homeopaths use different remedy potencies according to their experience and understanding of the case. Some prefer to begin a case with the low potencies, 6C or 12C, and slowly work up to the higher potencies. Some will usually begin a case with a 200C, 1M or 10m.
It can be generally stated, though, that in cases were there is a history or current use of medication, where the vitality of the patient is low or the remedy choice is not absolutely certain, then a lower potency will generally be chosen to start the case. Likewise, in very vital people with a clear case, and little or no history of medications, higher potencies are often used.