At my workplace, I've taught a number of younger colleagues how to solder. They come in with laboratory science degrees but varying levels of manual skills. I try to explain what makes a better soldering iron, and I think the 3 key ingredients are:
1. High quality plated tips with a reliable supply chain for replacements. Find a catalog supplier for the tips before ordering the iron.
2. A timer greatly promotes tip life if you're forgetful like me, and also placates colleagues / family members who are concerned about safety. Newer units have a built-in timer, older ones can use a cheap Belkin outlet timer.
3. Temperature control, which most soldering "stations" come with.
As for solder, lead-tin is easiest to use, but if you're committed to using lead-free, some alloys work better than others. I recommend Kester K100 as being the closest to "almost like lead-tin" due to a relatively low melting point and decent flow properties.
A magnifying visor or inspection microscope is extremely valuable for soldering fine pitch IC's.
Learning to be quick about forming a joint saves on melting the insulation of wiring and some delicate connectors.