Backpack or trolley case. I spent 20+ years carrying a laptop around either on commute to work, train or plane. In 2008 my shoulder decided it had enough, I was retuning on a plane from Canada when my shoulder seized up, I was off work for 4 months, I had a severe frozen shoulder, after physiotherapy a couple of cortisone injections I eventually returned to work. A surgeon who examined me an reviewed MRO scans & x-rays showed me the tendon damage in my shoulder, which in his opinion caused the damage and recommended I switched to a backpack to even the weight distribution out.
On my return to work the backpack laptop carrier was on my desk the day I returned, however I still suffer from a sore shoulder from time to time.