deadlifts and squats are two of the best core buliders u can do IMO
if u want to further improve it, avoid using machines and where possible do ur exercises standing up or with no back rest
ie instead of doing seated shoulder press witha bar bell do it standing up etc.... u will generally lift less unsupported though
If u wanna protect ur back, build up slowly and dont go too hard to quick... and if u are performing these exercises and u feel even a slight tweak in ur back FOR GOD SAKE STOP!!...ur only goin to make a small tweak worse and its goin to be alot sorer when u cool down