If you want to work on primary cells I also recommend you fibroblast cells, since the are easy for isolation, culture and growth. From one isolation you can recieve a lot of fibroblast cells that you can divide into aliquots, freeze and use for further practice with students!
Anything that grows fast, is durable and likes cheap media. E.g. HeLa, as mentioned by Frances and Harald, I'd like to add HEK293, 3T3 mouse fibroblasts, HT1080 fibrosarcoma. What's available or what you may grab from the lab next door.