MOTM

I'd like to order a pound of each type of solder included with the MOTM
kits, so that way the solder I use for my diy projects has the exact same
feel in order to produced the most consistent results.

I'm guessing the "organic" is Kester 331 - 63/37 alloy mix, .020" dia.,
core 66, guage 66.  Is that correct??

According to Moe's informative website, the "no clean" included with the
kits is Kester 245 with a .05 dia.  That's not listed in the Techni-Tool
catalog.  However, they do list four types of .031" diameter:  63/37 with a
core of 50, 58, and 66; and 60/40 with a core of 58.  Which is my best
choice??   What does "core" specify??