The diameter isn't all that important. Get the size that best fits your application.
I've been a tech for over half a century. Mostly DOD, with the Army, Air Force, and then Navy. We got refresher courses on soldering biennially, and tested annually. 63/37 is when solder meets the perfect "plastic" state for flowing and adhesion. 60/40 is slightly cheaper, or lazy labeling. It would be ok for guitar work. We just wouldn't use it for a guidance system in an F-14 or a Peacekeeper missile. (Their name, not mine.)