Golfception arrives

Python 3.6, 250 bytes

Saved 4 bytes thanks to isaacg, and 1 thanks to KoishoreRoy!

d=700                    # Current distance
from random import*
r=randrange              # Function that gets a random value in the range [0, input)
i=0                      # Number of strokes
while d:
 i+=1;x=r(20)<1          # x is False 95% of the time
                         # My justification for reusing this random value
                         # is that it's used once and only once, separate by if/elif
 if d<10:d-=[d,d*.75][x] # We're within putting range; goes in if x is true; otherwise makes 75% progress
 elif x:i+=1             # Goes in the water, add a stroke
 elif d<250:
  s=r(95);d-=[d,d*[.7+r(21)/100,.9*r(10)/100][s<15]][s>0]
                         # Only 95 because we already checked to see if it would go in the water
                         # 99% of the time (s>0), it doesn't go in
                         # 14% of the time (s<15), it makes 90-99% progress
                         # Otherwise, it makes 70-90% progress
 else:d-=250+r(101)      # Lose 250-350 yards
 d=int(abs(d));print(f'{d}m')
print(f'Total hits {i}')

Try it online! (Uses Python 3.5 printing syntax at a cost of 6 bytes since TIO does not yet support Python 3.6.)

Perl 6, 212 bytes

my&p=(^*).pick;say 'Total hits ',(700,->\d{my \n=d>249??abs d-(p(20)??250+p
100!!0)!!d>9??d-(|((d*(70+p 21)div 100) xx 80),|((d*(90+p 10)div 100) xx
14),d,|(0 xx 5))[p 100]!!p(20)??d div 4!!0;"{n}m".say;n}...0)-1

&p is a helper function that picks a random number from 0 to one less than its argument. The expression after 'Total hits ' is a lazily-constructed list that generates each element based on the previous element. The elements are printed as they are generated, which isn't very functional, but it is shorter than storing them in an intermediate array.