Rather than 60/40, I suggest Kester #44 63/37 0.031" rosin-core solder. It's better than anything else I've encountered over the decades. https://www.amazon.com/Kester-24-6337-0027-Solder-Alloy-Diameter/dp/B0149K4JTY/ -- It's available from Mouser and other real actual distributors but that's about the best price I found on a quick search back when I bought more. Unlike 60/40, 63/37 ("eutectic") doesn't have as much of a paste period in its cooling where the tin is molten but the lead is solid, so it's harder to get a "cold joint" from inadvertent motion of the soldered component fracturing the paste.

Which board..? If DNA, appropriate wire gauges will be listed in the data sheet.

But generally, 16-12 gauge for the high current stuff & 24-20 gauge for low current stuff.

Unless you have a specific reason for lead free solder, leaded will flow much better: https://www.amazon.com/gp/product/B0149K4JTY/

Would recommend some additional flux also: https://www.amazon.com/gp/product/B00425FUW2/ (clean up with isopropyl alcohol & qtips - even thought it says "no clean")