Selecting the correct footwear is really important. You will spend all of the time on your feet and if your feet aint happy then you wont be happy nor enjoy it. (How many enjoy the Y3P? :-) )
There are varying terrains, road, track, flagstones, rocky sections of up and down, Limestone and still plenty of wet areas.
I was up there in July, on DofE duty, and the water crossing the Y3P route up to Whernside was close to the top of our boots.
Most importantly the boots need to be chosen to fit the width and shape of your foot. Different manufacturers have different width lasts to manufacture their boots and walking trainers. Go to a quality Outdoor shop at a quiet time and explore options with the shop's boot fitter
Above all else get your footwear fitted to your feet. Buy a pair of socks at the same time and always use the same pair or same type of sock.
Good luck