Hi, with you back pain being insidious (over a period of time) in onset, most commonly it would involve tightness, weakness and postural imbalance.
Hence an exercise program should first address range of movement in all directions, low grade strength training which is then progressed. Good to start with lying, sitting and standing.
Situps can be an issue during early disc based injuries. However at later stages it could be done with adequate strengthening in extension also.
Posture during pushups is key. In simple words no sagging and chin poking.
Next Steps
some core stability training, which is not only abdominal strength training, nor is only planks....
Health Tips
take breaks in between work. posture with sitting is important.