I had lower back pain fracture which cured. I would like to lift weight due to flubby upper arms. Which is the best weight to buy?

Exercise/ back pain. The safest answer would be for you to use machine weights to minimize stress on your back. Tricep pulldowns and cable curls would achieve your goals.
Bicycle movements. For your arms. You can do them with a machine, you can do them with free weights. You can do them without any weights, just closing your fist and moving them like you are peddling a bicycle with your hands. Move from isometric contractions to a slow peddling motion, while contracting flexors and extensors. But be careful. This is very stressful on your heart and muscles.
See below. You can do them with a machine, you can do them with free weights. You can do them without any weights, just closing your fist and moving them like you are peddling a bicycle with your hands.