I use a Metcal STSS solder station with an STTC-126 series tip cartridge for pretty much everything (STTC-1xx series tip cartridges are 775°F). It's exactly what I, and everyone else, used when I worked in a PCB factory, for both surface-mount and through-hole soldering, and is a de facto industry standard of sorts. STTC-0xx (675°F) tip cartridges are available, but I don't know why anyone would use them except maybe for soldering some exotic ultra-low-temperature-handling parts that I'll never encounter.
I see the ~650°F recommendation thrown around a lot, but I can only assume that's because the thermostat-based temperature regulation of ordinary soldering stations with temperature adjustment dials is very loose, and setting it to 650°F gives you a large margin of error. The Curie point temperature regulation that Metcal tip cartridges use, combined with near-instant recovery time, keeps the tip at plus or minus a couple/few degrees of the target temperature when idling, and when rapidly dumping heat while soldering, it recovers to the target temperature almost instantly, but never exceeds it by any significant amount. So there's no need to worry about a margin for error.
For the record, the PCB factory I worked at, Edwards Systems Technology (
EST) built commercial fire alarm systems like you see in hospitals, factories, and such. Fire alarms are considered "life-saving equipment", and the manufacturing procedures are more tightly-regulated than if you were building e.g., radios (and they are also exempt from any ridiculous regulations that require lead-free solder). Everything we soldered was immediately tested in a
Hewlett Packard 3070 "bed-of-nails" machine, which tests every circuit/component on the PCB. If 775°F was too hot, STTC-1xx tips would not have been used there.
The solder we used was Alpha Metals Cleanline SMT Core Plus, P1 flux percentage, 63/37, .015" and .020" diameters. I still have a spool of it from work, but in the less useful .015" diameter (which we used for soldering the tiniest SMDs). I used that at home for many years, until I found a good deal on four 1-lb. spools of .020" a couple of years ago, which is way more than a lifetime supply for me: