1mm is an odd way to spec a wire...
Its not all that odd - it is used by more people world-wide than AWG is!
(And you have to be careful talking about wire gauge with the British, who
have their own wire gauge.
1mm is about #18 AWG.
In most cases the choice of stranded or solid depends on the application
and what is available. You shouldn't have a problem winding #18 solid wire
onto a toroid, and it will keep its shape better than stranded wire. But
for a thick wire you may find that stranded bends better to follow the
shape of the core. Whenever there is a lot of flexing, stranded wire is
better, but otherwise it usually doesn't matter all that much.