Had the modern breathable membrane stuff put in when we had our slate
roofs redone a few years back on the basis that the normal sarking
rots eventually and doesn't withstand exposure at all well. ie you
loose a slate and the sarking fails where day light (and water) can
get in between the slates... Along the gutter line our roofers put
18" (maybe 2') wide DPM with the membrane stopping 6" or so short of
the slate edge on top of it. DPM doesn't degrade...

Had my roof reslated 2 years ago, with hand-finished Spanish slate -
very happy with it all round.

Similarly had Tyvek throughout the whole roof, with additional
waterproof felt/DPM on the lowest 18-24" and lapped into the gutters.

Inside the roof it is dry, there is occasional condensation but it
does dry out no vents as such but it's still pretty drafty up
there... The lofts is much brighter as well, membrane is a light
colour rather than
dark.

My roofspace is bone dry, all year round, no condensation. No roof
vents, though there is an original (1873) arrow-slit type vent in the
brickwork on one gable end.

My additional tip would be don't skimp on the detailing - leadwork,
chimney & other flashings, chimney maintainence, gutters, fascias &
soffits etc - get the lot done at the same time.

Get it all specified in the contract, and accept there may be cost
overruns if it becomes apparent additional remedial work is required.
Swallow the cost and get it all done.