Best Approach to Loose Skin and Fat on Upper Arms?

Based on the photograph that you posted, its difficult to assess how heavy your arms are. For patients with heavy arm tissues and loose skin, I recommend a staged arm liposuction followed by arm lift 2-3 months later. The scars appear to be better in this sequence.

Your photo shows both excess of fat and skin of the upper arm that will not be resolved satisfactorily with liposuction alone.  I recommend a combination of liposuction and surgical skin reduction that can be safely done in one setting.  Your elasticity at your current age may not be adequate to tuck the incisions into the axilla alone, you should consider a longitudinal ellipse to be excised that would carefully place the closure on the inside surface of the arm.