Aaah, this is really not a good beginner's guide to soldering! Cranking up to max temperature might work a lot of the time but runs the risk of frying ICs and causing PCB traces to come off. Also using a wet sponge can cause the tips to rust. It's much better to clean them with a brass "sponge" leaving the tip tinned to protect it. Finally the real key to easy soldering is solder flux (and leaded solder if you're all…
If you use a moderate temperature (650°F/340°C) it's a gentler way to clean flux residue off the tip.
Brass wool I reserve for scrubbing oxidation off the tip, but this eventually wears through the plating so I don't do this often.
Leaded solder is both toxic and completely unnecessary for hobbyist use. I like SAC305 but SN99.7 works well too—the key is a good quality flux core.
No-clean flux is convenient but if you do want to clean it, it's gummy and makes a mess. "Yes-clean" flux leaves conductive residue so it must be cleaned, but it is easier to clean.
As far as temperature goes, the better your iron is at transferring heat, the lower the tip temperature you can use, which improves tip life and, as you mention, reduces the chance of part damage.
I am a lead dev on an open-source hardware project (PhobGCC) and I've seen damage caused by bad soldering irons time and time again. Don't cheap out. I recommend a Weller WE1010.