Could be ignition, caused by bad contact in the coil 12V feed, but
unlikely, as the car runs fine once it starts. Coil and ignition faults
are intermittent, and persistent, unlike this case.
I'd look to fuelling.
Outdoors, in good ventilation, attach a plastic
pipe to the fuel pump outlet. Crank and see if it starts pumping
immediately at cranking speed. There is usually a rubber link in
the fuel pipe between the tank pipe and the engine fuel pipe.
This is to absorb engine movement and prevent repetitive
flexing of the metal pipes. This perishes, becomes porous,
then you are sucking air at cranking speed. Once started
car runs fine. Obviously you lead the plastic pipe into a
bottle or jar.

Re wipers. Two possibilities, bad slipring contacts in the wiper
gear box. Water forced past the O-ring seal at speed has got
into the wiper shaft. Iron shaft, water, zinc diecast tube,
bad corrosion combination.  Dismantling and refurbishment
a pain in the butt. Replace with new or breakers yard unit.
Or it may be just unsuitable wiper blades that are age
hardned and worn.

For ignition problems there are little neon testers that sit
between plug top and lead. (not very bright) flash when
there is a spark. Cost 2 quid or so. When it cranks and won't
start, check to see if it flashes. If so you know it's unlikely
to be ignition if you see a spark. Only caveat bridged, oiled,
carbonised plugs also show ignition flash.