Dumbphones usually have an option to store contacts on the SIM or in phone memory. In my experience they also have the option to copy contacts between the two. When I've switched phones in the past (including to my first smart phone), my solution was always to transfer the lot to SIM card (frankly I kept them there already on my own phone), then when you pop the SIM card into the new phone, it can import them (assuming the new phone isn't lame), or simply read them directly off the SIM card and keep them there.
Storing contacts on the SIM card has two limitations I'm aware of:
1) 100 contacts max
2) 11 chars max for contact name