Best solder wire - Sn63Pb37 vs Sn60Pb40 vs ...?

Sn63/Pb37 is better than 60/40 because it is a eutectic alloy. That means it has the lowest melting point of any Sn/Pb alloy, and it solidifies relatively abruptly at one temperature rather than over a range. Generally both are advantages or neutral.

Combinations with small amounts of (say) gold tend to be for reducing the tendency of solder to dissolve the material (gold in this case).

Many solders these days avoid the use of lead and are often mostly tin with other materials such as copper, bismuth, silver etc. This is done to reduce the toxicity of electronics that finds its way into the waste stream. In my experience it is worse in every way compared to tin/lead solder except perhaps in applications where high melting temperature is important.

Flux another matter- there are a number of different types.

If RoHS compliance (and toxicity) are of no concern, 63/37 Sn/Pb solder with RMA rosin flux is an excellent choice, and is good for high reliability applications. Fine for hand soldering or reflow.

For production for world markets, it may be necessary to use lead-free solders with more finicky temperature profiles and inferior performance. Sometimes water soluble or no-clean fluxes are acceptable, depending on the product and how much it might affect the process (and possibly the product functionality).

Solderability has more to do with oxidized copper surface and choice of flux to reduce oxidation and tombstoning.

I recall the Eutectic or lowest temp solder mix is 63/37.

In some cases solder contamination with antimony can result in poor joints.

But the temp differences are minor compared to; surface prep, cleanliness , choice of flux , storage temp of paste, open air time, shelf life; pad design for reflow, board preheater (frying pan or IR oven, or ?) and hot air or radiant heat profile curves with thermocouple and lack of turbulence but smooth flow.

These all affect wetting, burn rate of volatiles, surface tension, shorts, opens, tombstone, etc. and be sure pad design is optimized for reflow, and thermal profile.

Also ensure DRC has been done before design is sent out and checked by board shop.

From a practical perspective, the main difference between the two is that the 63/37 is a eutectic alloy. In short, that means that it has a single melting point and not a plastic range like the 60/40 solder.

For prototyping and hobbyist use, it's really more a question of preference. If you are soldering wires together for example, 63/37 is easier to use because it will solidify faster and not cause cold solder joints. However, if you are soldering surface mount components on a pcb by hand, then the plastic range of 60/40 can help as that allows the components to "snap" into place.