I'm hoping the Sim card will be accessible when I get the next phone

Helen, from my recollection of less than smart phones it depends on how you save the phone numbers, and what the phone provided as choices. On one phone I remember asking to put them on the SIM card as well as the phone. The phone could save more numbers than the SIM card. Best of luck.

If the phone has a micro USB for charging, there is a chance the data can be accessed wherever, so ask your independent phone shop they will have the apps to do it.