The biggest difference is that an improperly soldered leaded joint looks very obviously wrong, whereas a good lead-free joint can be pretty much indistinguishable from a bad one.
If you are just starting out - and will therefore by definition have a poor iron, cheap solder, and poor technique - leaded is definitely the way to go. Once your first spool of leaded runs out, it is probably time to switch to lead-free.
The "shiny" aspect is the only way an improperly soldered joint can look the same on lead-free, and as a lead dev on an open-source hardware project that attracts a lot of people new to soldering, I have never ever seen a non-shiny leaded solder joint that wasn't horrendously bad in many other ways.
When a joint is bad, you get obviously poor wetting and weird mushroom shapes, but even so a newbie will not really notice that even using leaded solder.
If you are starting out, and you have a poor iron, cheap solder, and poor technique, you have already made two grave mistakes. We always urge people starting out to shell out in the $50 range for something that won't actively make them suffer, and they do just fine with SAC305.
I often mix up the shininess of leaded solder with the shininess of tacly flux under a ring-lit microscope. Can be hard for me to know if the joint is complete or partly made of goo.
The cloudy diffuse look of lead-free SAC305 is more distinctive to my eye.
If you are just starting out - and will therefore by definition have a poor iron, cheap solder, and poor technique - leaded is definitely the way to go. Once your first spool of leaded runs out, it is probably time to switch to lead-free.