I vote for W>0 when work is done *on* the system (energy enters)
as the default convention, to be modified when convenient (if
desired) when discussing engines. I think it's generally less
confusing to students if Q and W are both positive when energy
enters. I find this convention much more natural when discussing
chemical reactions, and chemical reactions are often important in
physics! It's also more convenient in refrigeration and many
other applications.
This convention actually is already used in many physics textbooks.
I have on my shelf two British books on thermodynamics (Mandl
and Carrington), and both do it this way. So does the excellent
book Atmospheric Thermodynamics by Bohren and Albrecht. And the
introductory text Six Ideas that Shaped Physics by Tom Moore.
And my own book, for what it's worth.