You are fairly save with a 15W soldering iron if the component leads take the solder well. Sometimes, when one uses recycled old components, the leads are a little tarnished and do not solder well. Better to clean them first by wiping with fine emery cloth than cooking them 'clean' with the soldering iron
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A few soldering tips: As a rule semi conductors are the most heat sensitive components. The smaller the item the more sensitive. What I do when assemblying them onto a printed board or a vero board is to leave the 'legs' intact for soldering and snip the excess part off after. That way the 'leg' acts as a heat sink during soldering.
If you are soldering expensive, multi legged, components it pays to get the soldering done right the first time, double check if the part is the right way round oriented or use an IC socket.
It is during de soldering that most components get excessively heated. For that reason, use the braid for the the bigger components such as connectors and such. Use a manual solder sucker for single hole unsoldering. These gadgets are not expensive and work well if cleaned out regularly.
For IC unsoldering, if its a PC board with plated through holes the best way is a bit insert that heats all the pins at once, but these need a temperature controlled iron of at least 60Watts. For ordinary two layer or vero boards you can use a solder sucker and free one pin at a time.
Do your soldering by simultaneously applying heat at one side of the component leg and the PCB track while introducing the solder wire at the opposite side. This gives you the guarantee the join was hot enough and the solder flowed freely with a fresh load of flux from the cores in it. With a bit of practice soldering goes very quickly with this method.
Never carry the solder on the tip of the iron to the solder joint, by the time it gets there the flux has evaporated and you get a lousy solder joint.
Have fun,
Klaus