There is no run in needed. All modern tips have plating. Keep the tip tinned generously all the time, except when actually soldering. It will last very long. Just before soldering, clean the tip with a wet sponge or brass wool, heat the point to be soldered and feed fresh solder to the area (you only want fresh solder that contains flux). Don't ever clean the tip mechanically with anything else than a sponge or brass wool.
If you happen to leave it on without the tip tinned, it might eventually oxidize. This can be remedied with applying lots of solder and repeatedly cleaning (sponge or brass wool). Additional flux might help, too. Do not use solder or flux that plumbers use, it contains corrosive acid flux that is bad for electronics. In worst case, I've managed to repair an old tip with special tip tinner paste, but it's some nasty stuff not to be regularly used.
As for leaded/lead free, it doesn't really matter for hobby use. But if you work for a company you should keep leaded and lead free tools separate. It's more of a certification thing than anything practical (except that lead is obviously not healthy for human bodies and that's why the whole lead free thing came to be).