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…
A wet sponge doesn't cause rust, it's occasionally blamed for cracking plating when you use a high temperature. 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 l…
Flux - hobbyists either try to use 50-year-old parts with totally oxidized plating and no flux, or they use too much flux. New parts should not need more flux than you have in your flux-core solder or in your paste.
The next thing that happens after people discover flux is that they want to clean it off, and 99% of the time, hobbyists should not be cleaning flux. If you cannot measure the reason for cleaning your board, leave it alone. The manufacturers will tell you that modern RA and RMA type fluxes do not require cleaning for "most applications" - and "most applications" almost certainly means you.
No-clean flux should be called "never-clean" for the reason you outline. You shouldn't try to clean it, and it will never get as clean as you'd like if you do. I like no-clean for stuff I'm going to show to other people. You will almost certainly use no-clean in production if you go to production.
Water-clean is lovely stuff but it's very unforgiving. It will corrode if not cleaned, and you have to plan to wash your board by using sealed parts or adding water-sensitive parts afterward. You have to be careful with tip temperature too or it will destroy your tips. I have a spool of 63/37 water-clean I've used maybe twice - the boards sparkled but it was just too much trouble.