I take a regular medication and I'm worried about continuity — will I be able to get it there, do I need a new prescription, how much do I bring? How did you handle ongoing meds across the move?
Get a doctor's letter listing your meds by their generic (not brand) names before you go — brand names differ between countries and it makes the first local appointment far smoother.
Carry enough to cover the transition plus that letter. Don't count on walking in and getting an instant local prescription for an ongoing medication.
Some meds that are routine at home need a local prescription elsewhere, or aren't available in the same form — check before you rely on it, and your new doctor can advise equivalents. Don't leave it to chance with anything essential.
Declare them properly when you travel, too — rules on carrying medication across borders vary and you don't want a problem at customs with something you need.
Generic-name letter + enough to bridge + check availability in advance. That's exactly the reassurance I was after — thank you all.