There is a nice picture of the "best" for different ranges of sizes of numbers to be multiplied at

http://gmplib.org/devel/log.i7.1024.png

More context and explanation can be found at: http://gmplib.org/devel/

BTW, I like Bernstein's survey of different multiplication algorithms at

https://cr.yp.to/papers/m3.pdf

(there is a unifying theme about using ring isomorphisms to explain many of the "standard" routines.)