Answer
Bring at least a two- to three-month supply of medications you take long-term. This is especially important for medications taken regularly and with a sufficient shelf life.
This supply is needed not to bypass local healthcare, but to ensure a smooth transition period. After moving, it will take time to choose a healthcare system, see a doctor, find a local equivalent, or obtain a prescription for the required medication.
First and foremost, bring anything you cannot suddenly go without: medications for ongoing treatment, rare medications, and medications that are difficult to replace. It is also useful to pack a standard first-aid kit, but the main priority is continuity of treatment during the first few months, while a local replacement has not yet been found.