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Personally, I'd suggested cmder[0]. It's much more light-weight than MobaXterm and doesn't require installation.

MobaXTerm doesn't require "installation", there's a portable version as well.

I've been a cmder user for years and love it... but AFAIK it doesn't have an SSH client built in?

See above - Windows does now! (and it already did if you were using WSL)

Ah, right, I see what you mean!